Wittgenstein: Understanding and Meaning: Volume 1 of an Analytical Commentary on the Philosophical Investigations, Part I: Essays (Pt. 1)

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Wittgenstein: Understanding and Meaning Part I: Essays

Other volumes of this Commentary

Wittgenstein: Rules, Grammar and Necessity, Volume 2 of An Analytical Commentary on the Philosophical Investigations G. P. Baker and P. M. S. Hacker Wittgenstein: Meaning and Mind, Volume 3 of An Analytical Commentary on the Philosophical Investigations Part I: Essays P. M. S. Hacker Wittgenstein: Meaning and Mind, Volume 3 of An Analytical Commentary on the Philosophical Investigations Part II: Exegesis §§243–427 P. M. S. Hacker Wittgenstein: Mind and Will, Volume 4 of An Analytical Commentary on the Philosophical Investigations Part I: Essays P. M. S. Hacker Wittgenstein: Mind and Will, Volume 4 of An Analytical Commentary on the Philosophical Investigations Part II: Exegesis §§428–693 P. M. S. Hacker Epilogue: Wittgenstein’s Place in Twentieth-Century Analytical Philosophy P. M. S. Hacker

Companion to this volume

Wittgenstein: Understanding and Meaning, Volume 1 of An Analytical Commentary on the Philosophical Investigations Part II: Exegesis §§1–184 G. P. Baker and P. M. S. Hacker second, extensively revised edition by P. M. S. Hacker

Volume 1 of An Analytical Commentary on the Philosophical Investigations

Wittgenstein: Understanding and Meaning

Part I: Essays

G. P. Baker & P. M. S. Hacker Fellows of St John’s College · Oxford

Second, extensively revised edition by P. M. S. Hacker

© 2005 by G. P. Baker and P. M. S. Hacker BLACKWELL PUBLISHING 350 Main Street, Malden, MA 02148-5020, USA 108 Cowley Road, Oxford OX4 1JF, UK 550 Swanston Street, Carlton, Victoria 3053, Australia The right of G. P. Baker and P. M. S. Hacker to be identiﬁed as the Authors of this Work has been asserted in accordance with the UK Copyright, Designs, and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs, and Patents Act 1988, without the prior permission of the publisher. This edition and Wittgenstein: Understanding and Meaning. Part II: Exegesis §§1–184 originally published together as Wittgenstein — Understanding and Meaning in 1980. First published in two volumes 1983 Second, extensively revised edition published 2005 by Blackwell Publishing Ltd Library of Congress Cataloging-in-Publication Data Baker, G. P. (Gordon P.) Wittgenstein : understanding and meaning / G. P. Baker & P. M. S. Hacker. — Second, extensively rev. ed. / by P. M. S. Hacker. p. cm. — (Analytical commentary on the Philosophical investigations ; v. 1) Includes bibliographical references and index. ISBN 1-4051-0176-8 (hardcover : pt. 1 : alk. paper) 1. Wittgenstein, Ludwig, 1889–1951. Philosophische Untersuchungen. 2. Philosophy. 3. Language and languages — Philosophy. 4. Semantics (Philosophy) I. Hacker, P. M. S. (Peter Michael Stephan) II. Title II. Series: Baker, Gordon P. Analytical commentary on the Philosophical investigations (2000); v. 1. B3376.W563P5323 2004 192—dc22 2004007861 A catalogue record for this title is available from the British Library. Set in 10/12pt Bembo by Graphicraft Ltd, Hong Kong Printed and bound in the United Kingdom by MPG Books Ltd, Bodmin, Cornwall The publisher’s policy is to use permanent paper from mills that operate a sustainable forestry policy, and which has been manufactured from pulp processed using acid-free and elementary chlorine-free practices. Furthermore, the publisher ensures that the text paper and cover board used have met acceptable environmental accreditation standards. For further information on Blackwell Publishing, visit our website: www.blackwellpublishing.com

For Anne and Sylvia

Contents Acknowledgements Introduction to Part I: Essays

xiii

Abbreviations

xix

I The Augustinian conception of language (§1) 1. 2.

3. 4. 5. 6.

Augustine’s picture The Augustinian family (a) word-meaning (b) correlating words with meanings (c) ostensive explanation (d) metapsychological corollaries (e) sentence-meaning Moving off in new directions Frege Russell The Tractatus

II Explanation (§6) 1. 2. 3. 4.

Training, teaching and explaining Explanation and meaning Explanation and grammar Explanation and understanding

III The language-game method (§7) 1. 2. 3. 4. 5.

The emergence of the game analogy An intermediate phase: comparisons with invented calculi The emergence of the language-game method Invented language-games Natural language-games

xi

1 1 4 4 6 7 9 11 14 19 23 26

29 29 33 35 39

45 45 54 57 61 63

viii

Contents

IV Descriptions and the uses of sentences (§18) 1. 2. 3. 4. 5.

Flying in the face of the facts Sentences as descriptions of facts: surface-grammatical paraphrase Sentences as descriptions: depth-grammatical analysis and descriptive contents Sentences as instruments Assertions, questions, commands make contact in language

V Ostensive deﬁnition and its ramiﬁcations (§28) 1. 2. 3. 4. 5. 6.

Connecting language and reality The range and limits of ostensive explanations The normativity of ostensive deﬁnition Samples Misunderstandings resolved Samples and simples

65 65 67 70 73 76

81 81 83 88 92 97 103

VI Indexicals (§39)

107

VII Logically proper names (§39)

113

1. 2. 3. 4.

Russell The Tractatus The criticisms of the Investigations: assailing the motivation The criticisms of the Investigations: real proper names and simple names

VIII Meaning and use (§43) 1. 2. 3. 4.

The concept of meaning Setting the stage Wittgenstein: meaning and its internal relations Qualiﬁcations

IX Contextual dicta and contextual principles (§50) 1. 2. 3. 4. 5. 6.

The problems of a principle Frege The Tractatus After the Tractatus Compositional theories of meaning Computational theories of understanding

113 117 120 124

129 129 136 144 152

159 159 164 170 171 173 181

Contents

X The standard metre (§50) 1. 2. 3. 4.

The rudiments of measurement The standard metre and canonical samples Fixing the reference or explaining the meaning? Defusing paradoxes

XI Family resemblance (§65) 1. 2. 3. 4. 5. 6. 7.

Background: deﬁnition, logical constituents and analysis Family resemblance: precursors and anticipations Family resemblance: a minimalist interpretation Sapping the defences of orthodoxy Problems about family-resemblance concepts Psychological concepts Formal concepts

XII Proper names (§79) 1. 2. 3. 4. 5. 6. 7.

Stage-setting Frege and Russell: simple abbreviation theories Cluster theories of proper names Some general principles Some critical consequences The signiﬁcance of proper names Proper names and meaning

XIII Turning the examination around: the recantation of a metaphysician (§89) 1. 2. 3.

Reorienting the investigation The sublime vision Diagnosis: projecting the mode of representation on to what is represented 4. Idealizing the prototype 5. Misunderstanding the role of the Ideal 6. Turning the examination around

ix

189 189 192 193 197

201 201 208 212 216 219 222 224

227 227 230 233 235 238 239 244

251 251 253 256 259 263 266

x

Contents

XIV Philosophy (§109) 1. 2. 3.

271

A revolution in philosophy The sources of philosophical problems The goals of philosophy: conceptual geography and intellectual therapy The difﬁculty of philosophy The methods of philosophy Negative corollaries Misunderstandings Retrospect: the Tractatus and the Investigations

284 287 290 294 299 303

XV Surveyability and surveyable representations (§122)

307

4. 5. 6. 7. 8.

1. 2. 3. 4.

Surveyability Precursors: Hertz, Boltzmann, Ernst, Goethe, Spengler The morphological method and the difﬁculty of surveying grammar Surveyable representations

XVI Truth and the general propositional form (§134) 1. 2. 3. 4. 5.

The demands of the picture theory ‘That’s the way the cookie crumbles’ ‘. . . do we have a single concept of proposition?’ (PG 112) ‘. . . the use of the words “true” and “false” . . . belongs to our concept “proposition” but does not ﬁt it . . .’ (PI §136) Truth, correspondence and multi-valued logic

XVII Understanding and ability (§143) 1. 2. 3. 4.

5. 6.

Index

The place of the elucidation of understanding in the Investigations Meaning and understanding as the soul of signs Categorial misconceptions of understanding Categorial clariﬁcation (a) Understanding is not an experience (b) Understanding is not a process (c) Understanding is not a mental state (d) Understanding is neither a dispositional state of the brain nor a disposition Powers and abilities Understanding and ability

271 277

307 311 320 326

335 335 340 344 346 349

357 357 359 362 367 368 369 371 373 375 380 387

Acknowledgements

While rewriting the essays of Wittgenstein: Understanding and Meaning, I have learnt a great deal from conversations and correspondence with friends and colleagues who were kind enough to read what I was writing and to comment upon it. I grateful to Dr Erich Ammereller, Dr Hanoch Benyami, Dr Leo Cheung, Dr Eugen Fischer, Professor Hans-Johann Glock, Professor Oswald Hanﬂing, Professor Roy Harris, Dr John Hyman, Sir Anthony Kenny, Professor Wolfgang Künne, Dr Oskari Kuusela, Dr Stephen Mulhall, Bede Rundle, Dr Severin Schroeder, Dr Joachim Schulte, Professor Herman Philipse and Professor Eike von Savigny, all of whom read and commented helpfully on one or more (some on many more) of the essays in this volume. They saved me from many errors, and alerted me to many problems. I am especially indebted to Edward Kanterian and Professor Herman Philipse, who read and commented constructively on almost all of the essays, and to Dr Jonathan Witztum, who not only read and commented upon the essay on family resemblance but also generously allowed me to read and make use of his own research work on this topic. And I thank those who attended my Friday afternoon graduate seminars and who asked searching questions. I am, as always, indebted to my college, St John’s, for its generous support of research and for the many facilities it provides. Jean van Altena’s admirable copy-editing has saved me from numerous infelicities, for which I am most grateful. ‘Contextual dicta and contextual principles’ was presented at a one-day conference at Southhampton University in April 2003 and at Utrecht University in April 2004. ‘Turning the examination around: the recantation of a metaphysician’ was presented at a conference on Wittgenstein in Venice in September 2002 and published in Wittgenstein at Work (Routledge, London, 2004), edited by Erich Ammereller and Eugen Fischer. A shorter version of ‘Surveyability and surveyable representations’ was published as ‘Übersichtlichkeit und Übersichtliche Darstellungen’, in a special edition of Deutsche Zeitschrift für Philosophie, edited by Professor Richard Raatzsch, to whom I am grateful for his constructive criticisms. P. M. S. H.

Thoughts reduced to paper are generally nothing more than the footprints of a man walking in the sand. It is true that we see the path he has taken; but to know what he saw on the way, we must use our own eyes. Schopenhauer

Introduction to Part I: Essays

The ﬁrst edition of Wittgenstein: Understanding and Meaning was written between 1976 and 1979. Gordon Baker and I intended it to be a comprehensive commentary on §§1–184 of Wittgenstein’s masterwork that would serve as a reference work for scholars intent upon a close study of the text. The essays attempted to give overviews of Wittgenstein’s treatment of speciﬁc themes. They aimed to trace the development of his thought, in particular contrasting his ﬁrst philosophy in the Tractatus with his evolving ideas in the 1930s and with the deﬁnitive statement of his later philosophy in the Philosophical Investigations. The exegesis attempted to explain Wittgenstein’s individual remarks, their role in the dialectic, and the structure of the evolving argument. For this purpose we traced their ancestry in his Nachlass, as best we could, making full use of the Cornell volumes of photocopied Nachlass that had been purchased by the Bodleian Library. As the years went by, further works of Wittgenstein came to light, some of them highly relevant to what we had written. Wittgenstein studies ﬂourished, and we learnt much from others who wrote on the same subjects. We also continued to work on the philosophy of Wittgenstein — together until 1987, and thereafter separately; and we came to realize that in various respects we had erred. We did not always agree on what we had misunderstood or on how what we had misunderstood should be understood. But some things that had seemed altogether opaque sometimes became, or seemed to become, clear. By the end of the century, we both thought that we should produce a thoroughly revised edition of the ﬁrst volume of the Commentary. With that project in mind, we approached Blackwell in June 2001, and were pleased to ﬁnd that they were willing to offer us a contract. Each of us was busy with other unﬁnished work at the time, but it was our intention to start work together on the revised edition in January 2002. The original joint project of the Commentary had come to an end after we had completed the second volume, Wittgenstein: Rules, Grammar and Necessity (1985), which took the Commentary as far as §242. Although we had planned to write Volume 3 together, fundamental differences of interpretation emerged between us. These differences were at the strategic — indeed, grandstrategic — level of our approaches to Wittgenstein, for they turned on our respective understandings of his philosophical methods and his overall conception of philosophy. Consequently they could not be avoided. We agreed

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Introduction to Part I

that I should continue the project alone. The third volume of the Commentary was published in 1990, and the fourth volume and the Epilogue, Wittgenstein’s Place in Twentieth-Century Analytic Philosophy, in 1996. When, in 2001, we decided to try to produce a second edition of Volume 1 of the Commentary together, we discussed our disagreements again. We hoped that we would be able to sidestep them, at least in dealing with the exegetical materials, and agreed that if, on any particular topic, that proved impossible, we would leave the original text as it stood. This was our plan. But it came to nothing. In December 2001, Gordon was found to have cancer, from which he died in June 2002. In the last months of his life, he was too unwell to participate in the project, and did not see any of the revised text of this volume. The rewritings and new writings that I present here reﬂect my understanding of Wittgenstein’s philosophy and my interpretations of his text. In view of the deep differences that had emerged between us in our interpretations of Wittgenstein’s philosophy, I must emphasize that Gordon Baker bears no responsibility for the many changes that I have made. Four different kinds of considerations weighed with me in my decision to produce a new edition of this book. First, since 1979, various primary sources and derivative primary sources have come to light and been published. MS 142, the ﬁrst draft of the Investigations §§1–189, written in 1936/7 in Norway, was rediscovered. The four volumes of post-war writings on the philosophy of psychology were published. Students’ lecture notes covering the years 1930 –2 and 1932–5 were edited by Desmond Lee and Alice Ambrose respectively, and notes of the last lectures on the philosophy of psychology were edited by Peter Geach. The Voices of Wittgenstein, dictations to Waismann for the project of The Principles of Linguistic Philosophy (Logik, Sprache, Philosophie), were edited by Gordon Baker. And various other lesser items have come to light over the last quarter of a century. In addition, a great deal of invaluable bibliographical work was done on the Wittgenstein manuscripts by Georg Henrik von Wright, Heikki Nyman, Joachim Schulte, Alois Pichler, Brian McGuinness and Stephen Hilmy. This clariﬁed the complex relationships between the different manuscripts and typescripts — many aspects of which were unknown when we ﬁrst wrote. There was much here that shed light on the exegesis of §§1–184 and on the subjects of the essays of the Commentary. Secondly, working on the Nachlass between 1976 and 1979 meant paging through more than 20,000 pages of photocopies of typescripts and, more importantly, of manuscripts, distributed over more than 100 volumes. Wittgenstein’s handwriting is often none too easy to decipher, and the Cornell xeroxes were woefully defective. In 2000 the Bergen project of transcribing the whole of the Nachlass into machine-readable form was completed, and it was published by Oxford University Press on CD-rom together with a search engine. In 2001 the ‘critical-genetic’ edition of the Investigations was published, edited by Joachim Schulte together with Heikki Nyman, Eike von Savigny and Georg

Introduction to Part I

xv

Henrik von Wright. It incorporates the various versions of the Investigations together with detailed editorial notes on the relationships between the drafts. All this has transformed the work of studying the development of Wittgenstein’s thought and interpreting his remarks. Thirdly, Volume 1 of the Commentary was a pioneering endeavour in Wittgenstein studies in making extensive use of the Nachlass to interpret his remarks and to trace the development of his ideas (preceded in this respect only by Garth Hallett’s A Companion to Wittgenstein’s Philosophical Investigations). We were then only beginning to ﬁnd our way around the Nachlass, and trying to ﬁnd our feet. In the later volumes the endeavour to trace the ancestry of individual remarks achieved a higher standard. That alone furnished a reason for doing a second edition, for I wanted to bring Volume 1 up to that standard. With the search engine, I could be conﬁdent of ﬁnding almost everything that I looked for (which, to be sure, is not the same as ﬁnding everything pertinent). The thought of tracing the source and evolution of every remark was a powerful incentive to undertake the labour. I was pleasantly surprised to ﬁnd that we had missed relatively little, and equally pleased to ﬁnd signiﬁcant new materials. The tables of sources in the volume of exegesis are now comprehensive and will, I hope, be of use to scholars. Furthermore, when working on the ﬁrst volume, we could not know where subsequent research on §§185–693 would lead. As I worked on the next three volumes during the subsequent ﬁfteen years, there were very many surprises and discoveries. Much of this, especially materials on intentionality used in Volume 4, shed important light on topics discussed in Volume 1. So I wanted to close the circle, as it were, to bring Volume 1 into line with the subsequent volumes. Finally, I had come to see numerous errors in what we had written 25 years ago. At the grand-strategic level, I saw no reason to change my mind. The guiding light for our interpretation of the Investigations in Wittgenstein: Understanding and Meaning was the co-ordination of meaning, understanding and explanation. This still seems to me to be correct. So too does the general conception of philosophy and philosophical method that we ascribed to Wittgenstein. However, at the strategic level there was much that was awry. The book bore the marks of the preoccupations of Oxford analytic philosophy in the 1970s. T-sentences and theories of meaning for natural languages stalked the wings and sometimes even stumbled on to the stage. And the account of Frege’s philosophy that we gave was strongly coloured by local interpretations that subsequently came to strike both of us as anachronistic. In this edition, these aspects of the book have been corrected. The discussions of Frege have been reduced in scope, and are intended to be as uncontroversial as possible. All views ascribed to Frege are backed up by ample textual evidence. An important strategic change has been a much reduced emphasis on the Augustinian conception of meaning. I continue to believe that this theme is important, and that it is indeed a (muted) leitmotiv running through the book. But its role

xvi

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was exaggerated in the ﬁrst edition, and its interpretation was, in certain respects, distorted. At the tactical level of interpretation of individual remarks, there were very many errors, and many things that needed examination were passed over. There were seventeen essays in the ﬁrst edition of this volume, and there are seventeen in the current edition. But two of the original essays have been dropped, and two new essays have been added. Many essays have been completely rewritten. Others have been substantially expanded in order to accommodate new materials, to reply to serious criticisms of Wittgenstein, to respond to signiﬁcant misunderstandings of his ideas, and to rectify errors of judgement and interpretation in the ﬁrst edition. The opening essay, now entitled ‘The Augustinian conception of language’ has been completely rewritten, with many changes of emphasis and argument. The essay on language-games, now entitled ‘The language-game method’, has been substantially expanded in order to explain the gradual emergence of the method and its relationship to other methods with which Wittgenstein experimented with in the early 1930s. In the ﬁrst edition, we thought that we could avoid the task of spelling out Wittgenstein’s conception of meaning as use. With hindsight, this was a misjudgement, which I have accordingly remedied with the essay ‘Meaning and use’. This new essay obviated the need for the ﬁnal essay of the original edition ‘Meaning and understanding’. The ideas in it have been distributed among other essays. The essay ‘A word has a meaning only in the context of a sentence’ has been replaced by ‘Contextual dicta and contextual principles’. Frege invoked a contextual principle not for one reason and one purpose, but for different reasons and different purposes. Although Wittgenstein quoted Frege’s dictum in the Tractatus, his motivation for his contextual principle differed from Frege’s, being picture-theoretic rather than function-theoretic, and when he quoted the dictum in the Investigations, its signiﬁcance and motivation were different yet again. So I have tried to tell the story of the various invocations of the dictum, and to explore its signiﬁcance. The essay on family resemblance has been substantially expanded to include an examination of the tradition of real deﬁnition and of Wittgenstein’s precursors in reacting against essentialism. The essay on vagueness and determinacy of sense has been dropped, and the ideas in it incorporated in the exegesis and essay on family resemblance. The two original essays on philosophy and methodology have been completely rewritten, and have been reinforced with a new essay entitled ‘Turning the examination around: the recantation of a metaphysician’. This, as intimated by the title, concerns Investigations §108 and the discussion leading up to it, which, as I have come to realize, contain some of Wittgenstein’s deepest reﬂections on the methodological sins of the Tractatus, written in 1936/7 especially for incorporation into the early draft of the Investigations. ‘Surveyability and surveyable representations’ replaces the earlier essay entitled ‘Übersicht’. It is much expanded, and traces the development of the idea of elucidation by overview more comprehensively than its

Introduction to Part I

xvii

precursor. The interpretation we had given of Wittgenstein’s conception of an overview and of the notion of a surveyable representation subsequently aroused grave doubts and misgivings in Gordon Baker. The new essay supports the old interpretation with detailed evidence from the Nachlass. ‘Truth and the general propositional form’, as signalled by its modiﬁed title, differs from its original. It examines the motivation for the conception of the general propositional form in the Tractatus. It then explains Wittgenstein’s reasons for repudiating that conception and investigates his views on truth and on multi-valued logic. In particular, it confronts the question of whether Wittgenstein cleaved to a correspondence theory of truth in the Tractatus, and how his later conception of truth is related to his earlier view. All the other essays have undergone various degrees of redrafting and compression, and often the addition of new material. Wittgenstein remarks in the Preface to his book that the nature of his investigation compels us to travel over a wide ﬁeld of thought criss-cross in every direction. Each of the pivotal concepts that he examines in order to resolve philosophical puzzlement is linked with numerous other concepts in the dense web of words. He is engaged, to use Strawson’s felicitous term, in connective analysis, and which connections require clariﬁcation and illumination depends upon the difﬁculty under consideration. One conceptual problem may demand that its local network be described from one direction, while another may require that the same reticulations be traced from a quite different direction. The essays in this volume that are intended to explain Wittgenstein’s thoughts display considerable overlap for the same reason. The concept of the meaning of a word, for example, is linked with that of explaining the meaning of a word, with using a word, with understanding what a word means, with the meaning of a sentence, and with what is meant by using a word and by uttering a sentence. As each of these nodes in the web is examined, its links with adjacent concepts require description afresh. That has unavoidably meant a moderate degree of repetition among the essays. Since the Commentary is not designed to be read through consecutively, and since I have tried to make each essay as self-contained as possible, the repetition is, I hope, excusable. The ﬁrst edition was published in a single hardback volume of 692 pages, in which the essays were dovetailed into appropriate places in the sequence of exegetical discussions of the individual sections of the Investigations. When the book was published as a paperback, it was split into two separate volumes, one of essays and the other of exegesis. This second edition is bifurcated from the beginning, the intended location of the essays in the exegesis being indicated in the table of contents of Part I, and in the text of Part II. Wittgenstein’s masterpiece is the most important work in philosophy since Kant’s Critique of Pure Reason. It is also as radical a work of philosophy as has ever been written, for it does indeed go down to the very roots of our thought. It is therefore not surprising that it is difﬁcult to understand. To follow Wittgenstein’s footsteps as he walks criss-cross over the wide landscape of ideas

xviii

Introduction to Part I

that he traversed requires much time and effort. This Commentary is written for those who are willing to spend the time and to make the effort. I hope that it will assist them in their quest for illumination.

P. M. S. Hacker St John’s College, Oxford October 2003

Abbreviations 1. Wittgenstein’s published works The following abbreviations, listed in alphabetical order, are used to refer to Wittgenstein’s published works. BB BlB BrB BT C CL CV EPB GB

LPE

LW I

LW II

NB PG

The Blue and Brown Books (Blackwell, Oxford, 1958). Occasionally used to refer to the Blue Book. Occasionally used to refer to the Brown Book. The Big Typescript, ed. and tr. C. G. Luckhardt and M. A. E. Aue (Blackwell, Oxford, 2005). On Certainty, ed. G. E. M. Anscombe and G. H. von Wright, tr. D. Paul and G. E. M. Anscombe (Blackwell, Oxford, 1969). Cambridge Letters, ed. Brian McGuinness and G. H. von Wright (Blackwell, Oxford, 1995). Culture and Value, ed. G. H. von Wright in collaboration with H. Nyman, tr. P. Winch (Blackwell, Oxford, 1980). Eine Philosophische Betrachtung, ed. R. Rhees, in Ludwig Wittgenstein: Schriften 5 (Suhrkamp, Frankfurt, 1970). ‘Remarks on Frazer’s “Golden Bough” ’, tr. J. Beversluis, repr. in Ludwig Wittgenstein: Philosophical Occasions 1912–1951, ed. J. Klagge and A. Nordmann (Hackett, Indianapolis and Cambridge, 1993), pp. 118 –55. ‘Wittgenstein’s Notes for Lectures on “Private Experience” and “Sense Data” ’, ed. R. Rhees, repr. in Ludwig Wittgenstein: Philosophical Occasions 1912–1951, ed. J. Klagge and A. Nordmann (Hackett, Indianapolis and Cambridge, 1993), pp. 202–88. Last Writings on the Philosophy of Psychology, vol. I, ed. G. H. von Wright and H. Nyman, tr. C. G. Luckhardt and M. A. E. Aue (Blackwell, Oxford, 1982). Last Writings on the Philosophy of Psychology, vol. II, ed. G. H. von Wright and H. Nyman, tr. C. G. Luckhardt and M. A. E. Aue (Blackwell, Oxford, 1992). Notebooks 1914–16, ed. G. H. von Wright and G. E. M. Anscombe, tr. G. E. M. Anscombe, 2nd edn (Blackwell, Oxford, 1979). Philosophical Grammar, ed. R. Rhees, tr. A. J. P. Kenny (Blackwell, Oxford, 1974).

xx

Abbreviations

PI

Philosophical Investigations, ed. G. E. M. Anscombe and R. Rhees, tr. G. E. M. Anscombe, 2nd edn (Blackwell, Oxford, 1958). PO Ludwig Wittgenstein: Philosophical Occasions 1912–1951, ed. J. Klagge and A. Nordmann (Hackett, Indianapolis and Cambridge, 1993). PR Philosophical Remarks, ed. R. Rhees, tr. R. Hargreaves and R. White (Blackwell, Oxford, 1975). PTLP Proto-Tractatus: An Early Version of Tractatus Logico-Philosophicus, ed. B. F. McGuinness, T. Nyberg and G. H. von Wright, tr. D. F. Pears and B. F. McGuinness (Routledge and Kegan Paul, London, 1971). RC Remarks on Colour, ed. G. E. M. Anscombe and G. H. von Wright, tr. L. L. McAlister and M. Schättle (Blackwell, Oxford, [1977] ). RFM Remarks on the Foundations of Mathematics, ed. G. H. von Wright, R. Rhees and G. E. M. Anscombe, rev. edn (Blackwell, Oxford, 1978). RLF ‘Some Remarks on Logical Form’, Proceedings of the Aristotelian Society, suppl. vol. 9 (1929), pp. 162–71. RPP I Remarks on the Philosophy of Psychology, vol. I, ed. G. E. M. Anscombe and G. H. von Wright, tr. G. E. M. Anscombe (Blackwell, Oxford, 1980). RPP II Remarks on the Philosophy of Psychology, vol. II, ed. G. H. von Wright and H. Nyman, tr. C. G. Luckhardt and M. A. E. Aue (Blackwell, Oxford, 1980). TLP Tractatus Logico-Philosophicus, tr. D. F. Pears and B. F. McGuinness (Routledge and Kegan Paul, London, 1961). Z Zettel, ed. G. E. M. Anscombe and G. H. von Wright, tr. G. E. M. Anscombe (Blackwell, Oxford, 1967). Reference style: all references to Philosophical Investigations, Part I, are to sections (e.g. PI §1), except those to Randbemerkungen (notes below the line) on various pages. Reference to these pages is given by two numbers, the ﬁrst referring to the page of the ﬁrst and second editions, the second to the third edition. References to Part II are to pages, in a like manner (e.g. PI p. 174/148). References to other printed works are either to numbered remarks (TLP) or to sections signiﬁed ‘§’ (Z, RPP, LW); in all other cases references are to pages (e.g. LFM 21 = LFM, page 21) or to numbered letters (CL); references to The Big Typescript are to the original pagination of the typescript as given in the Bergen electronic edition of Wittgenstein’s Nachlass (Oxford University Press, Oxford, 2000).

2. Derivative primary sources AWL LA

Wittgenstein’s Lectures, Cambridge 1932–35, from the Notes of Alice Ambrose and Margaret MacDonald, ed. Alice Ambrose (Blackwell, Oxford, 1979). Lectures and Conversations on Aesthetics, Psychology and Religious Beliefs, ed. C. Barrett (Blackwell, Oxford, 1970).

Abbreviations LFM LPP

LWL M

PLP RR VoW

WWK

xxi

Wittgenstein’s Lectures on the Foundations of Mathematics, Cambridge 1939, ed. C. Diamond (Harvester Press, Hassocks, Sussex, 1976). Wittgenstein’s Lectures on Philosophical Psychology 1946–47, notes by P. T. Geach, K. J. Shah and A. C. Jackson, ed. P. T. Geach (Harvester Wheatsheaf, Hemel Hempstead, 1988). Wittgenstein’s Lectures, Cambridge 1930–32, from the Notes of John King and Desmond Lee, ed. Desmond Lee (Blackwell, Oxford, 1980). G. E. Moore’s notes entitled ‘Wittgenstein’s Lectures in 1930–33’, repr. in Ludwig Wittgenstein: Philosophical Occasions 1912–1951, ed. J. Klagge and A. Nordmann (Hackett, Indianapolis and Cambridge, 1993), pp. 46–114. The Principles of Linguistic Philosophy, by F. Waismann, ed. R. Harré (Macmillan, London, and St Martin’s Press, New York, 1965). Discussions of Wittgenstein, by R. Rhees (Routledge and Kegan Paul, London, 1970). The Voices of Wittgenstein, transcribed and edited by Gordon Baker, tr. Gordon Baker, Michael Mackert, John Connolly and Vasilis Politis (Routledge, London, 2003). Ludwig Wittgenstein und der Wiener Kreis, shorthand notes recorded by F. Waismann, ed. B. F. McGuinness (Blackwell, Oxford, 1967). The English translation, Wittgenstein and the Vienna Circle (Blackwell, Oxford, 1979), matches the pagination of the original edition.

3. Nachlass All references to other material cited in the von Wright catalogue (G. H. von Wright, Wittgenstein (Blackwell, Oxford, 1982), pp. 35ff.) are by MS or TS number followed by page number (‘r’ indicating recto, ‘v’ indicating verso) or section number ‘§’, as it appears in the Bergen electronic edition of Wittgenstein’s Nachlass. In the case of the ﬁrst manuscript draft of the Investigations, MS 142 (the so-called Urfassung), references are to Wittgenstein’s section number (‘§’), save in the case of references to pp. 77f., which are redrafts of PI §§1–2 and to pp. 78 –91, which Wittgenstein crossed out and redrafted on pp. 91ff., subsequently assigning them section numbers in the redrafts alone. Manuscripts MSS 105 –22 are eighteen large manuscript volumes written between 2 February 1929 and 1944. These were numbered by Wittgenstein as Vols I–XVIII. In the ﬁrst edition of this commentary they were referred to by volume number, followed by page number (e.g. ‘Vol. XII, 271’). Since then it has become customary to refer to them by von Wright number alone. Here they are referred to on their ﬁrst occurrence in a discussion by their von Wright number, followed by volume number in parentheses, followed by page number

xxii

Abbreviations

as paginated in the Bergen edition (e.g. ‘MS 116 (Vol. XII), 271’). In the subsequent occurrence of a reference to the same volume in the same discussion, the volume number is dropped. ‘MS 114 (Vol. X) Um.’ refers to Wittgenstein’s pagination of the Umarbeitung (reworking) of the Big Typescript in MS 114. The Umarbeitung begins on folio 31v of MS 114 (Vol. X), and is paginated consecutively 1–228. Typescripts Bi Bemerkungen I (TS 228), 1945–6, 185 pp. All references are to numbered sections (§). B ii Bemerkungen II (TS 230), 1945–6, 155 pp. All references are to numbered sections (§). All other typescripts are referred to as ‘TS’, followed by the von Wright number and pagination as in the Bergen edition. The successive drafts of the Investigations are referred to as follows: TS 220 is the typescript of the Early Draft (Frühfassung (FF)) of the Investigations, referred to in the ﬁrst edition of this Commentary as ‘PPI’ (‘ProtoPhilosophical Investigations’), dictated from MS 142 (the Urfassung (UF)). TS 226R is Rhees’s pre-war translation of TS 220 §§1–116, referred to in the 1st edn of this Commentary as PPI(R). TS 227a and 227b are the two surviving carbon copy typescripts of the Investigations (the top copy having been lost). TS 238 is a reworking of TS 220, §§96 –116, with renumberings, deletions, corrections and additions in Wittgenstein’s hand, referred to in the 1st edn of this Commentary as PPI (A). TS 239 (the Bearbeitete Frühfassung (BFF)) is a reworking of TS 220. ZF is the reconstructed Intermediate Draft (Zwischenfassung) of the Investigations, previously known as the Intermediate Version, and referred to in the 1st edn of this Commentary as PPI(I). In transcriptions from the Nachlass I have followed Wittgenstein’s convention of enclosing alternative draftings within double slashes ‘//’.

4. Reference style to the other volumes of An Analytical Commentary on the Philosophical Investigations G. P. Baker and P. M. S. Hacker, Wittgenstein: Rules, Grammar and Necessity, Volume 2 of an Analytical Commentary on the Philosophical Investigations (Blackwell, Oxford and New York, 1985).

Abbreviations

xxiii

P. M. S. Hacker, Wittgenstein: Meaning and Mind, Volume 3 of an Analytical Commentary on the Philosophical Investigations (Blackwell, Oxford and Cambridge, Mass., 1990). P. M. S. Hacker, Wittgenstein: Mind and Will, Volume 4 of an Analytical Commentary on the Philosophical Investigations (Blackwell, Oxford and Cambridge, Mass., 1996). References to these are of the form ‘Volume’, followed by the volume number, the quoted title of an essay in the designated volume, and the section number of that essay. Occasionally reference to speciﬁc pages in an essay is made, in which case it is the paperback edition that is referred to. References to the exegesis are ﬂagged ‘Exg.’, followed by section number preﬁxed with ‘§’ or page number (in the case of the Randbemerkungen).

5. Abbreviations for works by Frege BLA i

BLA ii BS CN CP

The Basic Laws of Arithmetic, vol. i (1893); references to the preface by roman numeral indicating the original page number, all other references by section number (§). The Basic Laws of Arithmetic, vol. ii (1903); all references by section number (§). Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens (L. Nebert, Halle, 1879). Conceptual Notation and Related Articles, tr. and ed. T. W. Bynum (Clarendon Press, Oxford, 1972). Collected Papers on Mathematics, Logic, and Philosophy, ed. B. F. McGuinness (Blackwell, Oxford, 1984). To refer to individual articles in this volume, the following abbreviations are used: CO CT FC FG N SM T

FA NS

‘Concept and Object’ ‘Compound Thoughts’ ‘Function and Concept’ ‘Foundations of Geometry’ ‘Negation’ ‘Sense and Meaning’ ‘Thought’

All page references to these articles are to the original German pagination, as it occurs in the margins of the English translation, followed by the page number in CP. The Foundations of Arithmetic, tr. J. L. Austin, 2nd edn (Blackwell, Oxford, 1959). Nachgelassene Schriften, ed. H. Hermes, F. Kambartel and F. Kaulbach (Felix Meiner, Hamburg, 1969).

xxiv PMC

PW

Abbreviations Philosophical and Mathematical Correspondence, ed. G. Gabriel, H. Hermes, F. Kambartel, C. Thiel and A. Veraart, abridged for English edn by B. McGuinness, tr. H. Kaal (Blackwell, Oxford, 1980). Posthumous Writings, ed. H. Hermes, F. Kambartel, and F. Kaulbach, tr. P. Long and R. White (Blackwell, Oxford, 1979).

6. Abbreviations for works by Russell AM IMP IMT OK PLAt

PM PrM PP TK

The Analysis of Mind (Allen and Unwin, London, 1921). Introduction to Mathematical Philosophy (Allen and Unwin, London, 1919). An Inquiry into Meaning and Truth (Allen and Unwin, London, 1940). Our Knowledge of the External World as a Field for Scientiﬁc Method in Philosophy, rev. edn (Allen and Unwin, London, 1926). ‘The Philosophy of Logical Atomism’, repr. in The Philosophy of Logical Atomism and Other Essays 1914–1919, ed. J. G. Slater, in The Collected Papers of Bertrand Russell, vol. 8 (Allen and Unwin, London, 1986). Principia Mathematica, vol. i (with A. N. Whitehead), 2nd edn (Cambridge University Press, Cambridge, 1927). The Principles of Mathematics, 2nd edn rev. (Allen and Unwin, London, 1937). The Problems of Philosophy (Oxford University Press, London, 1967; originally published 1912). Theory of Knowledge: The 1913 Manuscript, ed. E. R. Eames in collaboration with K. Blackwell, in The Collected Papers of Bertrand Russell, vol. 7 (Allen and Unwin, London, 1984).

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

I

The Augustinian conception of language 1. Augustine’s picture The Investigations opens with a quotation from Augustine’s autobiography in which he describes how he thinks he learnt his mother tongue. The child, Augustine holds, perceives adults naming objects and moving towards things. Accordingly the child infers that such-and-such an object is signiﬁed by a given sound. So, as the child hears words used in sentences, he progressively learns what objects words signify, and in due course comes to use them to express his own desires. Wittgenstein detected in this description a picture or conception of the essence of human language: namely, that (i) words name objects, and (ii) sentences are combinations of words. It is evident that he thought this conception of naming as the essence of language to be of the ﬁrst importance (see Exg. §1). It is the natural way to think about language (MS 141, 1). After all, we teach our children that this is a horse, that this + n colour is called ‘black’, that doing this is what ‘run’ means, and so forth; and these are respectively names of an animal, of a colour and of an action. Pointing at an appropriate thing is a natural way of explaining what a given word means, and is widely used in teaching children. Further, we encourage the child to string words together in sentences, e.g. to say ‘The horse is black’ and ‘The black horse is running’. This pre-theoretical picture is manifest in the works of countless writers. Wittgenstein chose Augustine not because of the uniqueness of the conception, but because he was an exceptionally clear-thinking man, who belonged to a culture far removed from ours (MS 111 (Vol. VII), 15). If he too advanced this conception, then it must be important (see Exg. §1, n. 5). What makes it so important? It exhibits the roots from which numerous philosophical conceptions of meaning grow. It shows from what primitive picture or ‘world-picture’ a large range of misconceptions about language and linguistic meaning ﬂow (MS 111 (Vol. VII), 18).1 Moreover, such an idea of meaning was something which he, Wittgenstein, had ‘taken over’ (MS 114 Um. (Vol. X), 35), presumably from Frege and Russell. It informed the Tractatus, and was a source of many of its confusions. And it provides the counterpoint 1

This is not to say that Wittgenstein did not accept some of the points Augustine made. For elaboration, see Exg. §1.

2

The Augustinian conception of language

to the new conception of language and meaning advanced in the Investigations (see sect. 3 below). Being a natural way of thinking about language and language-acquisition, Augustine’s picture shapes the background presuppositions of much reﬂection on language by philosophers and linguists alike. It produces what Wittgenstein calls ‘a primitive philosophical conception of language’ or ‘a primitive philosophy of language’ (BT 25; MS 114 Um. (Vol. X), 35). How is this ‘primitive philosophy’ to be characterized? Above all, it conceives of naming as the essence of language (ibid.; MS 111 (Vol. VII), 15f.), and of the meanings of words as the foundation of language (MS 152, 38). In the Investigations, having characterized Augustine’s picture of language, Wittgenstein immediately moves on to a more self-conscious conception, which, he suggests, is rooted in Augustine’s pre-theoretical picture. According to this, (i) (ii) (iii)

every word has a meaning, this meaning is correlated with the word, the meaning of a word is the object it stands for.

This may be termed not ‘Augustine’s picture of language’, since Augustine made no such claims in the Confessions, but ‘the Augustinian conception of language’. It provides the point of departure for Wittgenstein’s investigations, and is a muted leitmotiv throughout his whole book. For although Augustine’s picture is not mentioned again after §32, the misconceptions associated with the ideas that the essential function of words is to name and that the meaning of a word is an entity for which a word stands are a recurrent theme not only in the Investigations but also in the Remarks on the Foundations of Mathematics (see Volume 2, ‘Two fruits upon one tree’). Is anything further associated with the Augustinian conception? Elsewhere explicitly, and in the Investigations implicitly (PI §6), Wittgenstein linked the Augustinian conception with a fourth claim: (iv)

the form of explanation ‘This is . . .’, i.e. ostensive explanation, constitutes the foundations of language (BT 25; cf. PLP 94f.).

This idea is another extension of Augustine’s picture, but, as already suggested, it is part of its natural appeal that we commonly teach children the meanings of words by pointing and saying ‘This is a so-and-so’. Finally, in Investigations §32, Wittgenstein links Augustine’s picture of language learning with a further idea: (v)

the child can think, i.e. talk to itself (in the language of thought, as it were), before it learns its mother-tongue from its parents.

Although the proposition that sentences are combinations of names is part of Augustine’s picture, it is striking that Wittgenstein does not incorporate any

The Augustinian conception of language

3

further claims about sentences into the ‘idea’ which he says is rooted in it. There can be no doubt that as far as Wittgenstein was concerned, the importance of Augustine’s picture lay in the conception of word-meaning which it presupposes. Nevertheless, Augustine’s idea of words as names and sentences as combinations of names, coupled with Wittgenstein’s elaboration, suggests a further step, which is no less fundamental to Wittgenstein’s early thought, and hardly less of a target of his later reﬂections (cf. PI §§27, 292, 317, 363, 577, 585): namely, that just as the essential function of words is to name things, so (vi)

the essential function of sentences is to describe how things are.

After all, he had once argued that the general propositional form is ‘Thusand-so is how things stand’ (TLP 4.5). The idea that describing is part of the essence of language is a natural corollary of the thoughts that the essence of words is to name things and that sentences are combinations of names. So although Wittgenstein himself did not explicitly incorporate this idea into the Augustinian conception,2 it will be explored later in this essay. The Augustinian conception of the essence of human language has moulded centuries of reﬂection. It is not itself a ‘theory of language’, let alone a ‘theory of meaning’. It is, rather, a framework of thought, a conception commonly taken for granted prior to systematic reﬂection. It is, as it were, the gravitational ﬁeld within which much European speculation on the nature of language has operated. Against the background suppositions that the essential function of words is to stand for things, that the things words stand for are what they mean, and that words are correlated with their meanings by ostension, which connects language to reality, many questions arise and are given a variety of different, often incompatible, answers. What they have in common is the unchallenged framework. In altogether characteristic manner, it is primarily this that Wittgenstein attacks — not so much the various doctrines and theses propounded by different, conﬂicting philosophies throughout the ages, but the common presuppositions. This will become evident in subsequent essays in this Commentary. But prior to examining Wittgenstein’s criticisms of such presuppositions, it is worth investigating some of the ways in which full-blown and 2

One reason why he may have omitted (vi) is that a magical aura and power surround the notions of names and naming, but not the ideas of description and describing. (Cf. MS 110 (Vol. VI), 177, quoted in Exg. §1, 2(i).) It should be noted that the fact that language-game (2) concerns only one-word imperatives (which are not descriptions), rather than corresponding one-word assertions, does not indicate that the idea that the essence of sentences is to describe is excluded from Wittgenstein’s account. For language-game (2) is deliberately tailored to ﬁt Augustine’s description in the Confessions (quoted in PI §1), not the ideas that Wittgenstein ﬁnds to be rooted in Augustine’s picture of the essence of language. For while language-game (2) is indeed ‘right’ for Augustine’s description, it is far from right for the Augustinian conception of language. Inter alia, the meanings of the names (‘block’, ‘pillar’, etc.) are not the building-stones — otherwise one might say that some meanings are cuboid and others cylindrical (see Exg. §2).

4

The Augustinian conception of language

articulate accounts of language can, according to Wittgenstein, be developed within this framework of thought.

2. The Augustinian family The following family of ideas is determined by two guidelines. First, the propositions advanced should be natural extensions of the more primitive picture. It is not that anyone who unreﬂectively cleaves to some or all of the above six principles will also adopt this whole family of ideas. Far from it. Indeed, some are inconsistent with others, being alternative lines of thought. Rather, these ideas can be considered to reﬂect a range of commitments indicative of a thinker’s operating under the inﬂuence of the principles of the Augustinian conception. Secondly, they should be directly related to arguments in Wittgenstein’s writings. The illustrations and exempliﬁcations in the footnotes are chosen to add substance and colour to the bare list of doctrines (many other authors could have been cited). Frege, Russell and Schlick apart, these quotations are not from authors Wittgenstein read (or, in some cases, could have read). They are meant to demonstrate the seminal importance of this conception of language — it is a seedbed from which numerous philosophies and theories of language grow. (a) Word-meaning (i) Every signiﬁcant word names (or signiﬁes) something.3 (ii) To have a meaning is to name some entity.4 To name something is to stand for or represent it. Of course, there may be words in a sentence that do not stand for anything, but they play a different role, e.g. a purely syntactical one (like ‘it’ in ‘It is raining’). (iii) The entity a word stands for is what it means. So the meaning of a word is the thing it represents.5 (iv) What kinds of entities word-meanings are is variously answered according to different pressures to which thinkers succumb. Certain pressures may induce one to think that words stand for various entities in reality — objects, properties, relations and so forth.6 Other pressures have inclined many

3

J. S. Mill: ‘It seems proper to consider a word as the name of that which we intend to be understood by it when we use it’ (System of Logic, Bk. I, ch. ii, sect. 1). 4 e.g. B. Russell: ‘Words all have meaning, in the simple sense that they are symbols which stand for something other than themselves’ (PrM 47). 5 e.g.: ‘A name means an object. The object is its meaning’ (TLP 3.203); or, put differently, ‘The meaning of Words, [are] only the Ideas they are made to stand for by him that uses them’ (Locke, An Essay Concerning Human Understanding, Bk. III, ch. iv, sect. 6). 6 e.g.: names ‘link the propositional form with quite deﬁnite objects’ (NB 53), ‘relations and properties, etc. are objects too’ (NB 61).

The Augustinian conception of language

5

thinkers to suppose that words stand for ideas in the mind of the speaker 7 (a tradition going back to Aristotle and made prominent by Locke and the British empiricists). Yet other pressures induce some theorists to hold that words stand for meanings conceived as abstract or psychological entities. (v) Words belong to different grammatical categories, e.g. proper names, common nouns, verbs, adjectives, adverbs. What category a given word belongs to is sometimes conceived to be determined by its meaning, i.e. by the kind of entity the word stands for. For surely the rules for the use of a word are answerable to the ontological category of what the word stands for.8 (vi) The grammatical category to which a word belongs determines its combinatorial possibilities in sentences. So its combinatorial possibilities are mediately determined by its meaning, by the entity for which it stands. It is as if a word were the coloured surface of a three-dimensional glass solid, the other surfaces of which are colourless and invisible. The visible forms that can be produced by their combination will be determined by the combinatorial possibilities of the invisible solids behind the visible surfaces. So too, the combinatorial possibilities of a word in sentences can readily seem to be determined by its invisible ‘meaning-body’ (Bedeutungskörper (see Exg. §138)). (vii) Words are conceived as standing for the entities that are their meanings. But nothing in Augustine’s picture or in the Augustinian conception determines whether they stand for meanings independently of their occurrence in a sentence or only in the context of a sentence. Should the picture and the conception that grows out of it be associated only with the former, atomistic variant? It is noteworthy that Augustine, in the quoted passage, emphasizes hearing ‘words repeatedly used in their proper places in various sentences’. Wittgenstein clearly thought of himself as having succumbed to the charms of the Augustinian conception, and arguably thought that Frege had too, but both were adamant that words have a meaning only in the context of a sentence. So, one may accept the basic principle that words stand for meanings, and opt for an atomistic construal of this, as Locke did, or one may opt for a context principle9 (TLP 3.3, 3.314; PI §49). Context principles may have very different motivations, e.g. function-theoretic in the case of Frege and picture-theoretic in the case of the Tractatus, and the dictum may be variously interpreted (see ‘Contextual dicta and contextual principles’, sects 2–3). (viii) The combinatorial possibilities in language reﬂect the combinatorial possibilities in reality of the objects that are the meanings of words. What is possible in language, as it were, mirrors what is possible in reality. On some 7

e.g. Locke: ‘Words, in their primary signiﬁcation, stand for nothing but the ideas in the mind of him that uses them . . . nor can anyone apply them as marks, immediately, to anything else but the ideas that he himself hath’ (Essay, Bk. III, ch. ii, sect. 2). 8 So Frege, e.g., held that rules for the use of expressions are answerable to the meanings (Bedeutungen) of the expressions: ‘the rules follow necessarily from the meaning of the signs’ (BLA ii §§91, 158; cf. PLP 234). 9 e.g. Frege: ‘Only in a sentence have the words really a meaning’ (FA §60).

6

The Augustinian conception of language

conceptions this is what would be true of a logically perfect language;10 according to others (most notably the Tractatus) it is true of language ‘on analysis’. (b) Correlating words with meanings (i) Every meaningful word is correlated with a determinate meaning. There are no indeterminate meanings, inasmuch as there are no indeterminate entities in reality. Whenever one uses a signiﬁcant word in a sentence to express a thought, one means something quite particular by it.11 (ii) Words are either deﬁnable or indeﬁnable.12 Deﬁnable words are explained by means of other words. Their meanings are given by specifying necessary and sufﬁcient conditions for their application. (iii) Indeﬁnables constitute the points at which language is directly linked with reality.13 They are connected with simple entities that are their meanings. These in turn may be conceived as simple ideas in the mind (e.g. Locke and the empiricists) or as simple natures (Descartes) or as simple objects that constitute the substance of the world (the Tractatus). Ultimately, all meaningful words derive their signiﬁcance from the connection between the indeﬁnables of language and reality. It is the indeﬁnables of language that, as it were, inject content into the web of language. (iv) Indeﬁnable words are directly connected with the given — either in inner or in outer sense.14 (v) When used in utterances, words are connected with their meanings either (1) by means of causation and association,15 or (2) by means of mental

10

Comenius, in Via Lucis (1688) (quoted by R. Simone, ‘The early modern period’, in History of Linguistics, ed. Giulio Lepschy, vol. iii (Longman, London, 1998), p. 173), held that an ideal philosophical language (‘Panglottia’) must be such that ‘its course is parallel with the course of things, that is, it contains neither more nor fewer names than there are things; and joins words to words with the utmost precision as things are joined to each other, by constantly expressing the nature of the things with which it deals by the very sounds which it uses, and so presenting them to the mind’. 11 As the young Wittgenstein thought: ‘But the sense must be clear, for after all we mean something by the sentence, and as much as we certainly mean must surely be clear.’ And ‘It seems clear that what we MEAN must always be “sharp” ’ (NB 67f.). 12 e.g. Locke: ‘The Names of simple Ideas are not capable of any deﬁnitions; the Names of all complex Ideas are’ (Essay Bk. III, ch. iv, sect. 4). 13 Names [i.e. logically simple names] ‘link the propositional form with quite deﬁnite objects. And if the general description of the world is like a stencil of the world, the names pin it to the world so that the world is wholly covered by it’ (NB 53). 14 e.g.: ‘The meaning [of indeﬁnables] must be given by direct acquaintance: one can learn the meaning of the word “joy” or “green” only by being joyful or by seeing green’ (M. Schlick, ‘The Future of Philosophy’, repr. in Gesammelte Aufsätze 1926–1939 (Gerold, Vienna, 1938), p. 129). 15 e.g. Russell: ‘The relation of a word to its meaning is of the nature of a causal law governing our use of the word and our actions when we hear it’ (AM 198).

The Augustinian conception of language

7

acts of meaning (intending) such-and-such an entity by the word16 (or interpreting the word of another as standing for such-and-such an entity). The causal conception of language is favoured by behaviourists and often also by classical associationist empiricists. The intentionalist conception is favoured by philosophers (including the young Wittgenstein) who have the problems of intentionality uppermost in their considerations. (c) Ostensive explanation The term ‘ostensive deﬁnition’ is of twentieth-century coinage. It ﬁrst occurs in W. E. Johnson’s Logic (1921).17 Equally, ‘hinweisende Deﬁnition’ emerged late, being preceded among members of the Vienna Circle by such cousins as ‘demonstration’ (Aufweisung) and ‘concrete deﬁnition’. Prior to the discussions of ostensive deﬁnition by members of the Vienna Circle (e.g. Schlick, Carnap, Waismann and Feigl) and Wittgenstein, one must look for analogues of what we today characterize as ‘ostensive deﬁnition’. If we go back to the empiricist debates about language that originated with Locke’s Essay, the analogue of ostensive deﬁnition is one or another variant of mental ostension whereby a word is associated with a mental sample or pattern.18 Recognition of the explanatory role of sentences of the form ‘This is A’ preceded their recognition as deﬁnitions, i.e. rules for the use of words. Hence the following enumeration of points moves gradually from ostension to ostensive explanation, and only then to ostensive deﬁnition. The recognition of ostensive explanation as a rule, together with the realization that it does not connect language with reality but remains, as it were, within language, that the sample pointed at belongs to the means of representation and not to what is represented, are decisive moves away from the Augustinian conception of meaning. (i) Ostension is the instrument for connecting language with reality; it ‘steps outside language’.19 Hence there must be ostensive explanations in any language, on pain of total vacuity.20 For it is by their means that content is injected into the web of words. 16

e.g.: ‘One could say, the intention is the method of projection’ (MS 108 (Vol. IV) 219; see also PR 65). For discussion, see ‘Turning the examination around: the recantation of a metaphysician’, sect. 2. 17 W. E. Johnson, Logic (Cambridge University Press, Cambridge, 1921), Part I, ch. VI, sect. 7. 18 e.g. Locke: ‘Such precise, naked appearances in the mind [viz. abstract general ideas], without considering how, whence or with what others they came there, the understanding lays up (with names commonly annexed to them) as standards to rank real existences into sorts, as they agree with these patterns, and to denominate them accordingly’ (Essay, Bk. II, ch. xi, sect. 9). 19 e.g. Waismann’s Thesen: ‘A deﬁnition remains within language. Ostension steps outside language and connects signs with reality’ (WWK 246). 20 e.g. M. Schlick: ‘We conclude that there is no way of understanding any meaning without ultimate reference to ostensive deﬁnitions’ (‘Meaning and Veriﬁcation’, repr. in his Gesammelte Aufsätze, p. 341).

8

The Augustinian conception of language

(ii) Ostensive explanation involves pointing at something and saying, ‘This is A’, thus connecting the word ‘A’ with the object that is its meaning. (iii) The thing pointed at may be conceived to be an object described by the sentence ‘This is A’,21 or it may be conceived to be a sample or pattern.22 (iv) Ostensive explanation explains inasmuch as the word ‘A’ can then be applied to anything that resembles the object or pattern pointed at.23 (v) The status of ostensive explanation may be variously conceived. A behaviourist conception will view it as having only a causal and pedagogic role in language acquisition. It is part of the training that establishes a child’s disposition to respond appropriately to stimuli, both verbal and non-verbal. It is an instrument for bringing about understanding of observation sentences.24 Alternatively it may be viewed as having a normative role in linking words with their meanings in reality (vide Locke, n. 18 above). Idealist conceptions of language take mental ostension to link words exclusively with mental representations or ‘ideas’ in the mind. Other conceptions take ostensive explanations to link non-psychological words with entities (objects, properties, relations) in extra-mental reality. In the case of our psychological vocabulary, however, words for unanalysable psychological attributes are commonly conceived to be linked to the attributes that are their meanings by association or intention.25 (Private ostensive deﬁnition is a sophisticated variant of this conception; see Volume 3, ‘Private ostensive deﬁnition’.) (vi) Ostensive explanations or deﬁnitions must be ﬁnal, the termini of explanations of meaning. Other forms of explanation of meaning ultimately depend on ostensive explanations, since only the latter make contact with reality. (vii) Consequently, ostensive deﬁnitions must be unambiguous. Otherwise the web of language which they connect to reality would itself be radically indeterminate. If an ostensive deﬁnition were ambiguous, or left open 21

e.g. W. V. Quine: ‘What characterizes direct ostension, then, is that the term which is being ostensively explained is true of something that contains the ostended point’ (‘Ontological Relativity’, repr. in Ontological Relativity and Other Essays (Columbia University Press, New York, 1969), p. 39). 22 See Locke, quoted above, n. 18. 23 e.g. R. Carnap: ‘ostensive deﬁnitions: here the term is deﬁned by the stipulation that the objects comprehended by the term must have a certain relation (for instance, congruence or likeness) to a certain indicated object’ (Logical Syntax of Language (Routledge and Kegan Paul, London, 1937), p. 80). 24 Thus Quine: ‘Many expressions, including most of our earliest, are learned ostensively; they are learned in the situation that they describe, or in the presence of the things they describe. They are conditioning, in short, to observations’ (Philosophy of Logic (Prentice-Hall, Englewood Cliffs, NJ, 1970), p. 6). 25 e.g. Thomas Reid: ‘The simplest operations of our minds must all be expressed by words [that cannot logically be deﬁned]. No man can explain by a logical deﬁnition what it is to think, to apprehend, to believe, to will, to desire. Every man who understands the language has some notion of the meaning of those words; and every man, who is capable of reﬂection, may, by attending to the operations of his own mind, which are signiﬁed by them, form a clear and distinct notion of them’ (Essays on the Intellectual Powers of Man (Edinburgh University Press, Edinburgh, 2002), pp. 19f.).

The Augustinian conception of language

9

questions about the application of the deﬁniendum, it would require supplementation. Unless this were itself a further ostensive explanation, something other than ostensive deﬁnition would be necessary to secure the foundations of language. (viii) Ostensive deﬁnition must be complete, i.e. fully determine the use of the word it links with the world. This will appear all the more plausible if the meanings of words are conceived of as determining their use (a(v) and (vi) above). By connecting the word with the object it means, the use of the word must be ﬁxed. (ix) Synthetic necessary truths concerning unanalysable properties in reality ﬂow from the natures of the entities that are the meanings of simple names. If, for example, an ostensive deﬁnition gives a complete explanation of what each colour-word means, then the necessary truth that nothing can be red and green all over must ﬂow from the objective nature of the colours. Each of these colours must, as it were, get in each other’s way, so they cannot simultaneously occupy the same position, just as two people cannot sit on the same chair.26 (d) Metapsychological corollaries (i) Knowing what a word means is knowing what object (entity, thing) is correlated with it as its meaning.27 (ii) Understanding a language is a mental state from which linguistic performance ﬂows.28 (iii) Using a word in an utterance with understanding, as opposed to mere parroting, is meaning something by it. Meaning something by a word is a mental act or activity whereby one projects the word on to the entity meant.29 26

‘That which corresponds in reality to the function “( ) PT” leaves room only for one entity — in the same sense, in fact, in which we say that there is room for one person only in a chair’ (RLF 169; cf. PR 106f.). (The function takes a colour or shade of colour as argument; ‘PT’ is a spatio-temporal speciﬁcation.) 27 A striking version of this principle, coupled with d(vi) below, is exhibited by Russell’s account of understanding names of ‘particulars’: ‘in order to understand a name for a particular, the only thing necessary is to be acquainted with that particular. When you are acquainted with that particular, you have full, adequate and complete understanding of the name, and no further information is required’ (PLAt 179). 28 Thus Noam Chomsky: ‘To know a language, I am assuming, is to be in a certain mental state, which persists as a relatively steady component of transitory mental states. What kind of mental state? I assume further that to be in such a mental state is to have a certain mental structure consisting of a system of rules and principles that generate and relate mental representations of various types’ (Rules and Representations (Blackwell, Oxford, 1980), p. 48). 29 Thus Locke: ‘Parrots, and several other Birds, will be taught to make articulate Sounds distinct enough, which yet, by no means, are capable of Language. Besides articulate Sounds therefore, it was farther necessary, that he should be able to use these Sounds, as Signs of internal Conceptions; and to make them stand as marks for the Ideas within his own Mind’ (Essay, Bk. III, ch. 1, sect. 3). Evidently making words stand for ideas is a matter of intending, ‘a voluntary Imposition, whereby such a Word is made arbitrarily the Mark of such an Idea’ Bk. III, ch. ii, sect. 1).

10

The Augustinian conception of language

The act of meaning is intrinsically intentional. Meaning or intending is the method of projection (n. 16 above). (iv) Understanding the words of another is knowing what he means by them. Knowing what he means by them is interpreting his words correctly. All successful communication by means of language involves interpretation.30 (v) Acts of meaning and of interpreting (understanding) are what give life to the otherwise ‘dead signs’ of language. The intentionality of language is derived from the intrinsic intentionality of these mental acts or activities. (vi) Knowing what an indeﬁnable means requires acquaintance with the object or entity that is its meaning. One cannot know what colour-words mean without having had the experience of seeing colours, what sensation-words (e.g. ‘pain’) mean without having had the corresponding sensation, or what emotion terms (‘anger’, ‘joy’, ‘fear’) mean without having felt the emotion. If ostensive deﬁnition is the foundation of language, then acquaintance is the foundation of understanding.31 This conception generates difﬁculties with the indeﬁnable (unanalysable) categorial expressions of a language (cf. Locke’s struggles with ‘substance’). Various options may be essayed, ranging from innateness (actual or virtual) to denial that categorial concepts stand for any object or entity (e.g. identiﬁcation of categorial expressions with variables, as in the Tractatus). Further difﬁculties are generated by other expressions, e.g. logical ‘indeﬁnables’ (primitive terms of logic). Russell, ever audacious, demanded ‘logical experience’ or ‘acquaintance with logical objects’ (TK 97). (vii) If an ostensive explanation is conceived to be a description (c(iii)), then grasping what an indeﬁnable word means is a matter of guessing the intended meaning of a constituent word in an assertion.32 (viii) If knowing what a word means is knowing what object it stands for, and if such knowledge is Russellian knowledge by acquaintance, then there cannot be degrees of understanding. For there are no degrees of (Russellian) acquaintance with simple objects that are ‘given’. (ix) Consequently, knowledge of the meaning of an unanalysable word is achieved, if at all, at a stroke. It consists in acquaintance with the entity that is the meaning of an indeﬁnable, and grasping the connection between the 30

This conception was arguably implicit in the Tractatus. It came to dominate Anglophone analytic philosophy of language in the second half of the twentieth century, although for reasons relatively detached from the motivations of the Tractatus and of the Augustinian conception of meaning. According to Donald Davidson, ‘We interpret a bit of linguistic behaviour when we say what a speaker’s words mean on an occasion of use’ (‘Belief and the basis of meaning’, repr. in Inquiries into Truth and Interpretation (Clarendon Press, Oxford, 1984), p. 141). 31 e.g. Locke: ‘Words being voluntary Signs, they cannot be voluntary Signs imposed by him on Things he knows not. That would be to make them Signs of nothing, sounds without Signiﬁcation. A Man cannot make his Words the Signs either of Qualities in Things, or of Conceptions in the Mind of another, whereof he has none in his own’ (Essay, Bk. III, ch. ii, sect. 2). 32 As Wittgenstein put it, if ‘this is A’ is already a proposition, then ‘it can only be understood once the meaning of “A” is known, i.e. I must now leave it to chance whether he takes it as I meant it or not’ (PR §6).

The Augustinian conception of language

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word and the entity that is its meaning. This appears to be something that occurs in a moment. It remains opaque how such an instantaneous event (i.e. grasping the meaning) can have effects that unfold thus over time (see PI §139), as one subsequently uses the expression in all the variety of sentences in which it may be used. (x) In order for us to acquire a language, we must, in some sense, already possess one — an idea that has been at the centre of late twentieth-century linguistic theory.33 Hence too, thought, no matter of what degree of complexity, must appear to be antecedent to and independent of mastery of a public language. Public language will then seem to be necessary not for thinking, but rather for the communication of thoughts.34 Thought-constituents, i.e. the cogitative analogue of words, will have meanings quite independently of words of a public language. Speaking will be conceived to be a matter of translating from the language of thought into a public language. So speaking with thought will seem to consist of two parallel, concurrent processes: thinking and speaking (see Volume 3, ‘Thinking: the soul of language’, sect. 2). (e) Sentence-meaning Wittgenstein characterized Augustine’s picture of the essence of language as including the idea that sentences are combinations (not lists) of names. In his explicit triadic expansion of Augustine’s picture into the Augustinian conception, and in his two addenda, nothing further is mentioned about sentences. Nevertheless, as we shall see, the thought that just as the essence of words is to name, so too the essence of sentences is to describe invites incorporation into the Augustinian conception. Accordingly, it is worth reﬂecting on some of the ways in which various philosophical conceptions of the nature, role and understanding of sentences grow naturally out of the primitive ideas of words as names of entities that are their meanings, and of sentences as combinations of words.

33

‘The speed and precision of vocabulary acquisition leaves no real alternative to the conclusion that the child somehow has the concepts available before experience with language and is basically learning labels for concepts that are already part of his or her conceptual apparatus.’ And ‘the child approaches language with an intuitive understanding of such concepts as physical object, human intention, volition, causation, goal, and so on. These constitute the framework of thought and language, and are common to the languages of the world . . . it is beyond question that acquisition of vocabulary is guided by a rich and invariant conceptual system, which is prior to any experience’ (N. Chomsky, Language and the Problems of Knowledge (MIT Press, Cambridge, Mass., 1988), pp. 27f. and p. 32). 34 e.g. Hobbes: ‘The general use of speech, is to transfer our mental discourse, into verbal; or the train of our thoughts, into a train of words’ (Leviathan, Pt. 1, ch. 4). So too Locke: ‘The Comfort and Advantage of Society, not being to be had without Communication of Thoughts, it was necessary, that Man should ﬁnd out some external sensible Signs, whereby those invisible Ideas, which his thoughts are made up of, might be made known to others. . . . Thus we may conceive how Words, which were by Nature so well adapted to that purpose, come to be made use of by Men, as the Signs of their Ideas’ (Essay, Bk. III, ch. ii, sect. 1).

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(i) Sentences, being combinations of names, are, as has been argued ever since Plato and Aristotle, composite.35 Accordingly, one-word sentences are elliptical (see Exg. PI §§19f.). (ii) The meaning of a sentence must be determined by, or be a function of, the meanings of its constituent words. Augustine emphasized that he learnt language by hearing the words ‘repeatedly used in their proper places in various sentences’. It is natural to follow such a thought through and to take the meaning of a sentence as a function of the meanings of its constituents and their mode of combination (‘aRb’ obviously does not describe the same circumstance as ‘bRa’). (iii) If the signiﬁcant words in a sentence are correlated with entities that are their meanings, it seems natural enough to suppose that the arrangement of words in a sentence represents a possible arrangement of the things named.36 Of course, this possibility may not obtain. (iv) If the arrangement of things that are correlated with the words of a sentence is in fact the arrangement speciﬁed by the sentence, then what the sentence says is true. This conception lends itself to variants of the correspondence theory of truth, according to which truth consists in a relation of correspondence between proposition and fact.37 It can, however, be exploited without any such commitment, and it is noteworthy that the Tractatus did just that: the fact that p is held to make true the proposition that p, but truth is not conceived to consist in any relationship. Rather, as Wittgenstein put it (ungrammatically) ‘p is true’ = ‘p’ (NB 9), or, more happily, a proposition is true if things are as we, in using it, say they are (TLP 4.062, modiﬁed translation; cf. the rather interesting formulation in NB 113).38 A picture (of which 35 e.g. the Port-Royal Logic: ‘Judgements are propositions expressed by sentences . . . sentences themselves are composed of words . . . The product of judging is expressed by a sentence which must contain two terms — the one term is the subject, which expresses the idea of which we afﬁrm or deny another idea; the second term is the predicate, which expresses the idea which is afﬁrmed or denied of the idea expressed by the subject’ (A. Arnauld, The Art of Thinking, tr. J. Dickoff and P. James (Bobbs-Merrill, Indianapolis, 1964), Pt. II, chs 1–3). So too Mill: ‘Now the ﬁrst glance at a proposition shows that it is formed by putting together two names. A proposition . . . is, discourse, in which something is afﬁrmed or denied of something. . . . every proposition consists of two names; and every proposition afﬁrms or denies one of these names, of the other’ (System of Logic, Bk. I, ch. i, sects 2 and 3). Very differently, and for very different reasons, ‘What constitutes a propositional sign is that in it its elements (the words) stand in a determinate relation to one another. A propositional sign is a fact’ (TLP 3.14). 36 ‘The conﬁguration of objects in a situation corresponds to the conﬁguration of simple signs in the propositional sign’ (TLP 3.21). 37 e.g. Russell: ‘Thus a belief is true when there is a corresponding fact, and is false when there is no corresponding fact’ (PP 75). So too Moore: ‘To say that this belief is true is to say that there is in the Universe a fact to which it corresponds; and to say that it is false is to say that there is not in the Universe any fact to which it corresponds’ (Some Main Problems of Philosophy (Allen and Unwin, London, 1953), pp. 276f.). 38 The Tractatus conception is a precursor of Ramsey’s deﬂationary account of truth, sometimes called ‘the redundancy theory’ (although not by Ramsey). For discussion, see ‘Truth and the general propositional form’, sect. 5.

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a proposition is a special case) is true if what it depicts is the case (not if it corresponds to what is the case). (v) Since the same words, correlated with the same entities as their meanings, can occur in sentences of very different syntactical forms, e.g. declarative, interrogative, imperative, it is plausible to think that all such sentences can be bifurcated, on analysis, into the co-ordinated names expressing a sense and another element signifying that things are being asserted to be thus, or that the speaker is asking whether things are thus, or that the speaker wants things to be thus. Hence some kind of distinction between mood-operator (force-indicator) and descriptive component (sentence-radical) is a fairly natural outgrowth of the Augustinian conception.39 (vi) Hence too, the thought that description is part of the essence of a sentence is also a natural one, even though imperatives and sentence-questions do not superﬁcially look as if they describe anything. So a natural addendum to Augustine’s idea that the essence of words is to name is the further idea that the essence of sentences is to describe. Declarative sentences describe how things stand and are used to assert that they do so stand; imperative sentences describe how things do not stand and are used to order or entreat that things be made to stand thus; and interrogative sentences describe an arrangement of things and are used to ask whether that is how things stand. (vii) If the meanings of words are conceived to be entities in reality with which words are correlated, and if the combinatorial rules of grammar are reﬂections of, and determined by, the combinatorial possibilities of those entities, then it is plausible to explain why certain combinations of words are nonsensical by reference to their meanings. So, the reason why it makes no sense to say ‘The colour red tastes salty’ is because the colour red cannot combine with tastes; i.e. the meanings of these words cannot be combined (the meaning-bodies will not ﬁt).40

39

e.g. Russell: ‘In all these [viz. “Beggars are riders”, “Beggars would be riders”, “Are beggars riders?” and “Beggars shall be riders”], the relation between beggars and riders is the same; but in the ﬁrst it is asserted, in the second suggested as a consequence of a hypothesis, in the third the object of a doubt, and in the fourth the object of a volition. . . . they all have something very important in common. The word “proposition” is a natural one for expressing what they all have in common: we may say that they express different attitudes towards the same “proposition”. . . . we may express the proposition by the phrase “beggars being riders”’ (TK 107). 40 Taking the proposition ‘Two is a prime number’, Frege wrote: ‘The ﬁrst constituent, “two”, is a proper name of a certain number; it designates an object, a whole that no longer requires completion. The predicative constituent “is a prime number”, on the other hand, does require completion and does not designate an object. I also call the ﬁrst constituent saturated; the second, unsaturated. To this difference in the signs there, of course, corresponds an analogous one in the realm of meanings: to the proper name there corresponds the object; to the predicative part, something I call a concept. . . . An object, e.g. the number 2, cannot logically adhere to another object, e.g. Julius Caesar, without some means of connection. This, in turn, cannot be an object but rather must be unsaturated’ (FG I (CP 281 (371f.)).

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(viii) The meaning of a sentence being a function of the meaning of its constituent words and their mode of combination, one arrives at an interpretation of another person’s utterance by deriving the meaning of the sentence from one’s knowledge of the meanings of its constituents and their mode of combination.41 Understanding another’s utterance is therefore a computational process.42 The various ideas sketched above do not constitute, and are not meant to constitute, a single or a complete account of language and linguistic meaning. They are a variety of offshoots that can grow from the ideas that are rooted in Augustine’s picture of the essence of language, and the adoption of a signiﬁcant number of them by a thinker is indicative of the extent to which he is operating within the framework of such presuppositions. That conception could be elaborated in further ways. The propositions mentioned above and illustrated by quotation were selected because they demonstrate the importance of the Augustinian conception, its attractive power, and its ubiquity in the thought of writers throughout the ages who have reﬂected on linguistic representation.

3. Moving off in new directions It is evident that Wittgenstein thought the Augustinian conception of the nature of language and linguistic meaning to be exceedingly important. As we shall see, it is plausible to view the Tractatus, and indeed the works of Frege and Russell, as moving in the gravitational ﬁeld of this conception. Certainly he thought it sufﬁciently important to combat root and branch. For these ideas are attacked in the Investigations, and the host of auxiliary ideas that constitute the Augustinian family are assailed too, if not there, then in his other writings. It would be misconceived to suppose that all Wittgenstein was concerned with was to cure us of this syndrome of confusions, i.e. to get us to abandon our misconceptions, without replacing our confusions by something better — that is, by a ﬁrmer grasp of the conceptual structures in this domain of reﬂection. To be sure, he does not offer us a ‘theory of language’, let alone a ‘theory of meaning for a natural language’ — ideas he would surely have repudiated. What he does offer us are grammatical clariﬁcations of the concepts and reticulations of concepts of name, word, meaning of a word, meaning something by a word, 41

e.g. Frege: ‘The possibility of our understanding sentences we have never heard before rests evidently on this, that we construct the sense of a sentence out of parts that correspond to the words’ (PMC 79). 42 Chomsky, e.g., argued that various grammatical principles are incorporated in ‘the mind/ brain’ as a ‘matter of biological necessity’, and that we then ‘determine the interpretation of [suchand-such] sentences by a computational process of unconscious inference’ (Language and Problems of Knowledge, p. 55; see also p. 90).

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explanation of word-meaning, ostensive deﬁnition, sample, sentence, sentencemeaning, uses of sentences, proposition and so on. These are not doctrines or theses, any more than propositions such as ‘Red is a colour’, ‘Nothing can be red and green all over’, ‘White is lighter than black’, ‘Nothing can be both white and transparent’ are doctrines or theses. Wittgenstein’s grammatical clariﬁcations will be examined throughout this Commentary. It may, however, be useful to sketch in advance some of the differences between the Augustinian conception (and the associated family of ideas), on the one hand, and Wittgenstein’s conception, on the other. For even a rough sketch of these contrasts may add chiaroscuro to the above account. A proper, and properly qualiﬁed, picture of Wittgenstein’s ideas on these matters will emerge from the subsequent essays and the detailed exegesis of his text. In place of the conception of word-meaning as determined by a word– world nexus, Wittgenstein now holds that the meaning of an expression is, with certain qualiﬁcations, its use in the practice of speaking the language (see ‘Meaning and use’, sect. 4). We should conceive of words not as names of entities of various logical kinds, but as tools with a variety of quite different uses. A language is a public, rule-governed practice, partly constitutive of the form of life and culture of its speakers. The meaning of a word is what is given by an explanation of meaning, and an explanation of meaning is a rule for the use of the word explained, a standard of correct use. To know what a word means is to be able to use it in accordance with generally accepted explanations of what it means, to be able to explain appropriately what it means and what one means by it in an utterance, and to be able to respond comprehendingly to its use by others. The idea that the essential function of words is to name entities, and hence that the basic question to be addressed regarding any given word is ‘What does it name?’ or ‘What logical type of entity does it stand for?’, is misguided. ‘All words are names of things’ is at best vacuous, at worst wrong. Words have a multitude of uses, fulﬁl a large variety of roles in speech. The questions that should be addressed by philosophers are, rather: ‘What is this word for?’, ‘What need does it meet?’, ‘How would one teach its use?’, ‘What counts as a correct explanation of its use?’ — the answers to such questions will show what it is for a word to have a meaning. Similarly, it is misconceived to suppose that the essential function of sentences is to describe. If we think thus, we shall again be prone to ask the wrong kinds of question. We may wonder what arithmetical sentences describe — relations between numbers, or between signs, or between mental constructions. We may ask whether geometrical sentences describe the properties of space or of Ideal ﬁgures in a Platonic realm. We may be inclined to think that logical propositions describe relations between propositions or the most general facts in the universe, and that deontic propositions describe what ought to be done. But we should be asking what roles arithmetical, geometrical and logical propositions fulﬁl, what function they have (see Volume 2, ‘Grammar and necessity’), and what the point of deontic propositions is.

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The Augustinian conception of language

This reorientation has dramatic corollaries. There is, in the relevant sense, no connection between language and reality. Of course, this does not mean that we do not refer to things ‘in reality’ when we speak. What it means is that the picture of language as deriving its content from the primitive indeﬁnables that are correlated with objects in the world is misconceived. So the conception of ostensive explanation or deﬁnition as the instrument that effects such a correlation is itself awry (see ‘Ostensive deﬁnition and its ramiﬁcations’, sect. 3). The meaning of a word, even if the word can be said to stand for something, is not the object it stands for. And many kinds of word cannot usefully be said to stand for anything. The meaning of a word, like the price of a good, is not an entity of any kind. A word stands to its meaning in a manner akin to the relation between a coin and its use (not the relation between the coin and an object purchased). Explanations of meaning are very various (see ‘Explanation’, sect. 3). Neither analytic deﬁnition nor ostensive deﬁnition enjoy special privileges. Analytic deﬁnition is not the ideal towards which all explanations of meaning should strive. Many words — indeed, many words that occupy a special position in philosophical reﬂection — are family-resemblance terms, and are not explained by analytic deﬁnitions (see ‘Family resemblance’). Inability to give an analytic deﬁnition does not, in general, betoken lack of understanding. Many expressions are indeed vague, but that does not render them useless or transform propositions in which they occur into senseless concatenations of words. Ostensive deﬁnitions specify only one rule among others for the use of a word. Indeed, they presuppose the grammatical category of the word deﬁned. They can be misunderstood, for they are not necessarily unequivocal. They do not connect language to its foundations, supposedly constituted by the ‘objects’ that are the meanings of simple names. Language has no foundations in the sense associated with the Augustinian conception (and explicit in the Tractatus), and the meanings of names are not entities of any kind. The whole picture of the web of language as having content ‘injected’ into it at the point where the indeﬁnables of language make contact with reality was a misconception. For language is, in this respect, a free-ﬂoating structure — it is not, in this sense, connected with reality. Hence too, the grammar of our language, far from reﬂecting the logical structure of the world or the objective, languageindependent nature of things, is autonomous (see Volume 4, ‘The arbitrariness of grammar and the bounds of sense’, sect. 4). It pays no homage to reality. The practice of speaking a language does not rest on meaning-endowing connections between language and reality, or on primitive indeﬁnables that inject meaning into the web of words. But it might be said to rest on natural human behavioural tendencies and pronenesses, common discriminatory capacities and shared reactive propensities. Speaking is acting, and presupposes the agency of living beings active in the stream of life. ‘What has to be accepted, the

The Augustinian conception of language

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given, is — so one could say — forms of life’ (PI p. 226/192; see Volume 2, ‘Agreement in deﬁnitions, judgements and forms of life’).43 Ostensive explanations are typically deﬁnitions, and deﬁnitions are not descriptions. ‘This + n is black’, if it is an ostensive deﬁnition, is not a true or false predication. It is a rule for the use of the deﬁniendum. Indeed, there is a patent kinship between this, and a substitution-rule as given in an analytic deﬁnition. For instead of the word ‘black’ in a true/false predication, one may use the sample, ostensive gesture and demonstrative, and say, e.g., ‘My shoes are this + n colour’. Far from ostensive deﬁnitions connecting language with reality, the sample which a typical ostensive deﬁnition uses belongs to the means of representation, and is not something described by the explanation.44 The sample with which an ostensive deﬁnition may be linked need not be a ‘simple object’. Indeed, the concepts of simplicity and complexity are relative, and have to be speciﬁed separately for each category of thing if it is to make any sense to speak of things of that category being either simple or complex. Hence too, the competence of ostensive deﬁnition is not restricted to so-called simple names. There is no reason why some words should not be explained in more than one licit way, e.g. by analytic and by ostensive deﬁnition. What appear to be synthetic necessary truths about colour, say — for example, that black is darker than white, or that nothing can be red and green all over simultaneously — are not descriptions of the a priori order of the world (indeed, there is no such thing (see ‘Turning the examination around: the recantation of a metaphysician’, sect. 5)). Their truth is not attributable to the objective, language-independent nature of things. Rather, such propositions, although they look like descriptions of de re necessities, are in fact rules for the use of the constituent words (see ‘Ostensive deﬁnition and its ramiﬁcations’, sect. 4). Precisely because language has no foundations in the requisite sense, and because ostensive deﬁnition ‘remains within language’ (cf. PG 97), the picture of language (ideal or analysed) as a mirror of the logical or metaphysical structure of the world is a mythology of symbolism. The world does not have a logico-metaphysical structure (there is no such thing). The thought that a fully analysed sentence or a sentence couched in an ideal notation matches or is 43

There are, to be sure, hosts of propositions and types of propositions that are taken for granted by members of a linguistic community such as ours. But these are not propositions about ‘the Given’ as traditionally conceived (e.g. about sense-data, or about indubitable Cartesian thoughts and simple natures). Rather they are propositions such as ‘The earth has existed for many years’, ‘Here is a hand’, ‘I am N.N.’, ‘12 × 12 = 144’ (which Wittgenstein discusses in On Certainty) — not foundations of knowledge, but unquestioned and unchallengeable pivots on which our noetic structure turns. 44 Of course, what was intended by A as an explanation of word meaning for B may be taken as a description by C, just as ‘It is also possible for someone to get an explanation of the words out of what was intended as a piece of information’ (PI, p. 18/16n.).

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isomorphic with what it describes is quite mistaken. It is based on a confused idea of word–world connections and deep misconceptions concerning intentionality (see Volume 4, ‘Intentionality’, sect. 5). Understanding an expression is not a mental state or an activity of interpreting. It is akin to an ability (see ‘Understanding and ability’, sect. 6). To know what a word means is to be able to use it correctly and to be able to answer the question ‘What does it mean?’, not to be acquainted with its meaning. The criteria for whether a person understands an expression are the use he makes of it (i.e. whether he uses it correctly), the explanations he gives of what, in a given context, it means, and the responses he makes to its use by others. Meaning something by a word or sentence is not an act or activity (see Volume 4, ‘The mythology of meaning’). Understanding the utterance of another is not typically interpreting, and where interpretation is called for, understanding is presupposed, since to interpret an utterance is to choose between alternative meanings. Understanding, not being an activity, is not a derivational or computational process either. Precisely because understanding is ability-like, there can be degrees of understanding, partial as opposed to complete mastery of the technique of using a word. Understanding something at a stroke is not a high-speed exercise of an ability (e.g. to derive or calculate), but the inception of the ability to do the various things the doing of which counts as satisfying the criteria of understanding. A sentence (with marginal exceptions) is the minimal unit for ‘making a move in the language-game’ (see ‘Contextual dicta and contextual principles’). But, contrary to what both Frege and the Tractatus had supposed, a sentence need not consist of combinations of words (a name of an argument and a name of a function). For there are one-word sentences. One may say that one-word sentences in our language are typically elliptical, since we can often paraphrase them into multi-word sentences. But it is easy to envisage primitive languages in which that is not so. Sentences have an indeterminate variety of functions. Although describing is one, it is misguided to think that describing is itself logically uniform (compare describing how things are with describing how they might be, how one dreamt of them as being, how they should be, etc.), and equally misconceived to suppose even that all declarative sentences have the role of describing. Firstperson psychological sentences are often avowals or expressions of experience, thought or will (see Volume 3, ‘Avowals and descriptions’). Arithmetical sentences are not descriptions, but rules, for example, for the transformation of empirical propositions about magnitudes and numbers of things. Geometrical sentences are not descriptions of the properties of space or of the properties of Ideal ﬁgures, but rules for describing, for example, spatial relations. And logical sentences are not descriptions of relations between thoughts (as Frege believed) or statements of the most general facts in the universe (as Russell held). They are senseless sentences that say nothing, but are internally related to rules of inference (see Volume 2, ‘Grammar and necessity’, sects 2,3 and 5).

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There are indeed systematic internal relations between assertions, questions and orders. The question whether p is answered by the assertion that p (or the assertion that not-p). The order addressed to N.N. to V is the order that is obeyed by N.N.’s V-ing. But these internal relations are readily explicable without recourse to the idea that corresponding declarative, imperative and interrogative sentences have a common descriptive content given by a sentence-radical, and are differentiated (on analysis) by their different ‘forceoperators’. The imperative ‘Shut the door!’ addressed to N.N. no more contains a description of N.N. shutting the door than the assertion that N.N. shut the door contains the question ‘Did N.N. shut the door?’, although, to be sure, one could adopt a convention whereby ‘N.N. shut the door’ was expressed by ‘Did N.N. shut the door? Yes’ (see ‘Descriptions and the uses of sentences’, sect. 3). Of course, there are combinations of meaningful words that make no sense. But that is not because the meanings of these words do not ‘ﬁt’ together. For again, the meanings of words are not entities of any kind, and there is no ‘meaning-body’ behind each signiﬁcant word. When a sentence is said to be nonsense, it is not its sense that it is nonsense (PI §500, see Exg.). Rather, words that do have a use in the language (unlike nonsense poetry) are being combined in illicit ways, and nothing has been stipulated regarding their use in such aberrant sentential contexts. To say that the sentence ‘It is ﬁve o’clock on the sun’ makes no sense is simply to say that this form of words has no use in the language. Of course, we could give it a use. But then the constituent words would mean something different from what they now mean (see Volume 4, ‘The arbitrariness of grammar and the bounds of sense’, sect. 5). Finally, there is, and could be, no such thing as ‘a language of thought’ (PG 144f., BB 34f.). Thoughts are not representations, and, unlike the case of genuine representations, it makes no sense for one to raise the question of what is meant by a thought one thinks. Thoughts, unlike representations, have no non-representational properties; they are, so to speak, all message and no medium (see Volume 3, ‘Thinking: the soul of language’, sects 1 and 3). Thinking is a widely ramiﬁed concept. Speaking with thought is not engaging in two activities simultaneously, and speaking thoughtfully is not translating from a language of thought into a public language. The relationship between thinking and the mastery of linguistic techniques is a complex one. But the horizon of possible thoughts is constituted by the limits of the possibility of the expressions of thoughts (ibid., sect. 3).

4. Frege It is not difﬁcult to show why Frege may be deemed to be operating within the framework of thought guided by the Augustinian conception of language. With marginal qualiﬁcations he held the following principles.

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(i) Every expression in his concept-script that contributes to the determination of a judgeable content or thought is a name of an entity of one kind or another.45 (i′) After appropriate parsing or paraphrase, every expression in a sentence of natural language that contributes to the determination of the judgeable content it signiﬁes or thought it expresses is the name of an entity of one kind or another. (ii) The entity which such an expression names is its content or meaning. (iii) Sentences themselves are names. In his later view, they have truthvalues as their meaning. (iv) Sentences are combinations of names. They are essentially complex, composed of argument- and function-names. (v) For purposes of logical analysis of inferences, a judgement (expressed by a sentence) has priority over its constituents. What entity a sub-sentential expression names depends, in some cases, on the manner in which the sentence is parsed (the content of judgement, or, later, the thought, analysed). For, in certain cases, one and the same judgement can be decomposed in different ways. So a word has a meaning only in a sentential context (BS §§9f.; PW 16f.; FA p. x, §§60, 62, 10646), where it fulﬁls a role in one or another way of bifurcating a sentence into function-name and argument-expression. (vi) The combinatorial possibilities of words in sentences are determined by the kinds of entities that are their meanings. Two objects cannot combine together without an unsaturated entity, such as a relation, to bind them together; therefore two proper names (singular referring expressions) cannot form a sentence. An object can combine with an unsaturated entity (such as a function), therefore a proper name can combine with a concept-word to form a sentence (see n. 40 above). (vii) Therefore, the rules for the use of words are answerable to the meanings of those words (see n. 8 above). (viii) Declarative and interrogative sentences split up into, or can be analysed into, a descriptive, truth-value-bearing component (e.g. ‘that p’, which Wittgenstein later calls ‘a sentence-radical’ (PI p. 11/9n.), and a forceoperator (roughly, ‘It is the case’ and ‘Is it the case’). The former speciﬁes the descriptive content of the sentence. So, description is part of the essence of declarative sentences (deﬁnitions apart) and sentence-questions. (See ‘Thoughts’, 62 (CP 355 (62)); ‘Negation’, 144, 147 (CP 373f. (143–5), 376 (147)).) 45

With such exceptions as free variables, the double-stroke of deﬁnition and the judgementstroke, every symbol of concept-script in a well-formed sentence (in The Basic Laws of Arithmetic) has a meaning, i.e. stands for something. ‘Every well-formed name must have a meaning’ (BLA i p. xii), and all logically signiﬁcant expressions (with these exceptions) are names, they stand for, mean or designate some entity (BLA i §§32f.). 46 In the Foundations the context principle is highlighted as the way to avoid slipping into psychologism and holding words, in particular number-words, to be names of ideas. Its roots, however, are in the priority of judgements over concepts in decompositional analysis.

The Augustinian conception of language

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These principles are characteristic of the Augustinian conception and its associated family of ideas. What is striking and important is that, unlike Hobbes and Locke, for example, Frege was not led to think thus by an unreﬂective commitment to the primacy of naming, or by the naturalness of ostensive explanation of meaning (in fact, Frege has no doctrine about ostensive explanation at all). He was a mathematician, with little interest in the so-called foundations of language in experience, and none in language-acquisition and teaching. So what led him to adopt an array of principles that conform so closely with the central commitments of the Augustinian conception and its related family? Frege’s philosophical goal was to demonstrate that arithmetic is reducible to pure logic. For this purpose he invented a new logical calculus, far more powerful than anything hitherto available. The drive-shaft of this formal system was the generalization of the mathematicians’ concept of a function (BS, Preface; CN 204f.; PW 16f., 26, 184; FC 21, 28; BLA i §2; PMC 59). Frege allowed objects in general as the arguments and values of functions, and represented judgeable contents (in his early system), and truth-values (in his later system) as the values of certain functions for arguments. Accordingly, sentences split up into argument-names and function-names. In simple atomic sentences, such as ‘a is F ’, the argument-expression ‘a’ is the name of an object, and the functionname ‘ξ is F ’ is the name of a function or concept. In quantiﬁed sentences, such as ‘Everything is F’, the argument-name ‘ξ is F’ is the name of a concept, and the quantiﬁer is the name of a second-level function that takes concepts as arguments and maps them on to judgeable contents (in the early works) or truth-values (in the later system). In his pre-1890s work, Frege speaks indifferently of sub-sentential expressions as having a content or a meaning. In his mature work, he splits his earlier notion of content into sense (Sinn) and meaning (Bedeutung).47 It is evident that, given Frege’s understanding of the concept of a function, the demands imposed by generalizing the notion of a function for the purposes of formalizing the logic of generality drove him to embrace the above principles that converge upon the Augustinian conception of language. For a function, he held, is a pattern of correlation of entities. With various qualiﬁcations, he conceived of every logically signiﬁcant expression in a sentence as standing for some entity or other — an object, a concept or a higher-level function. An expression that stands for an entity is held to be a name. So singular referring expressions that stand for objects are ‘proper names’; concept-words are held to be names of concepts; and quantiﬁers are said to 47

‘Bedeutung’, when used in Frege’s works in the early 1890s and later, is sometimes translated ‘reference’ (whereas when it occurs in the Foundations of Arithmetic it is translated as ‘meaning’). Translating it as ‘reference’ has no textual warrant (it is no less strained in German to talk of an object or person, e.g., as the Bedeutung of a proper name than it is to speak of an object or person in English as its meaning). Moreover, it is questionable whether the idea that every signiﬁcant expression in a well-formed sentence with a truth-value refers to an entity of one kind or another is an improvement over the thesis that every such expression stands for a meaning or content.

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be names of higher-level functions. The logical connectives too are names of functions. Negation is construed as a unary function; conjunction, alternation and conditionality as binary functions that map ordered pairs of truth-values on to a truth-value. Not only are the logically signiﬁcant constituents of a sentence (after proper parsing or paraphrase) all names of one kind of entity or another, but, further, the sentence itself is also held to be a name (of a truth-value). What motivated his descriptivist drift (i.e. (viii) above)? Again, it is the exigencies of the function-theoretic apparatus he employed, together with his conception of the workings of the grammar of natural language. In conformity with tradition, he thought that the assertoric force of a sentence is (confusingly and defectively) marked in the predicate, in the indicative mood of the verb (PW 184f., 198). But his conceptual notation eschewed subject/predicate parsing in favour of function/argument decomposition. So he felt it necessary to mark the assertoric force in some other way. He did so by embedding it in an assertion-sign preﬁxed to the sentence-radical that he thought was a constituent of every expression of a judgement or sentence-question. Did he think that sentence-radicals are descriptions? Certainly they are bearers of truth-values. Of course, this does not entail that he thought that they are descriptions, but it creates such a presumption. And if we examine Frege’s other discussions (especially ‘Thoughts’), that presumption is borne out. For it seems clear that he thought that sentences concerning physical objects are descriptions of the ‘physical world’ and that sentences concerning psychological phenomena describe the ‘mental world’. Arithmetical sentences describe the ‘third world’ of abstract objects, and logical propositions describe relations between the truth-values of thoughts (see ‘Thoughts’ (CP 351–72)). Following Kant, he held that geometrical sentences describe the properties of space in synthetic a priori propositions. Various classes of sentences are, therefore, differentiated not by their different roles or functions, but by reference to what they describe. Declarative sentences as different in function as ﬁrst-person avowals of experience, modal propositions (e.g. ‘Nothing can be red and green all over’), arithmetical equations, statements of geometrical theorems, and tautologies of logic are uniformly held to describe. Of course, one must concede that Frege did not think that every word or phrase in a sentence of natural language stands for an entity. In his view, some words fulﬁl a purely syntactical or formal role (e.g. the copula). Others stand for an entity only when taken together with the context of utterance (e.g. indexicals). Some words — for example, empty names — do not stand for anything. Some phrases do not do so either — for example, the subject terms of syllogistic, such as ‘All men’ in the sentence ‘All men are mortal’. But properly parsed or paraphrased — for example, ‘For all x’ and ‘if x is a man then x is mortal’ — every logically signiﬁcant unit here does stand for an entity. The other examples are no more than forms of context-dependency of natural language, or logical imperfections and opacities, that are all remedied in a logically adequate language, such as Frege’s concept-script, which excludes empty names and is both context-free and logically transparent.

The Augustinian conception of language

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Equally, one may concede that with his differentiation of sense from meaning, Frege severs meaning, thus construed, from the objects of understanding. Expressions in natural language can have a sense and no meaning, and two non-synonymous names can have the same meaning. But it is also clear that the notion of sense merely serves to reinforce other aspects of the referential picture. For the senses of expressions serve to determine what entity they stand for. A baroque ontology ensues. The realm of meanings includes not only objects, but also concepts, relations and further functions of various levels. The population of objects is swelled to include such ‘entities’ as numbers, classes, directions of lines, truth-values, the simultaneous occurrence of events, and even the senses of sentences (which are construed as the meanings of that-clauses in reported speech). In short, both the misuse of the concept of meaning (Bedeutung) and the commitment to the idea that the essential function of words or phrases (properly parsed) is to name entities for which they stand remains intact. So too does the descriptivist drift. Although Frege’s philosophy is far more sophisticated than the simple, and naive Augustinian conception, there is ample reason for thinking that it is one of Wittgenstein’s implicit targets in his criticisms of the various doctrines he associates with this conception of the essence of language. Frege’s philosophy of logic, precisely because it is inspired by a generalization of the mathematical conception of a function, is rooted in Augustinian soil.

5. Russell In the course of the ﬁrst quarter of the twentieth century, Russell changed his mind, with bewildering rapidity, on a host of matters in the philosophy of language and logic. Nevertheless, he adhered unswervingly to an array of fundamental ideas that can be characterized as aspects of an Augustinian conception of language and meaning. His ﬁrst major work, The Principles of Mathematics (1903), exhibited a naive form of the Augustinian conception of language. Subsequently, as he struggled with his theory of denoting complexes, and as the Theory of Descriptions emerged in response to those struggles, he moved away from this naive form towards something more subtle. He came to think that although natural language, in its surface grammar, does not conform to the principles of the Augustinian conception, on analysis, it does. Moreover, a logically ideal language, he argued, would perspicuously do so. (i) In the Principles, Russell asserted: ‘Every word occurring in a sentence must have some meaning’ and ‘Words all have a meaning, in the simple sense that they are symbols which stand for something other than themselves’ (PrM 42, 47). He was later to back off from this naive claim, arguing that many expressions (including ordinary proper names, deﬁnite descriptions, names of classes, etc.) are ‘incomplete symbols’ that do not actually stand for anything at all and, in that sense, do not have a meaning on their own. But when such

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expressions are replaced by their analysans, then the constituent words do stand for entities that are their meanings. (ii) In the Principles, Russell held that expressions may be deﬁnables or indeﬁnables. To understand indeﬁnables, such as ‘red’ or ‘sweet’, we must be acquainted with their meanings. So too, we must be acquainted with logical indeﬁnables. The discussion of these, he asserted, ‘is the endeavour to see clearly the entities concerned, in order that the mind may have that sort of acquaintance with them which it has with redness or the taste of a pineapple’ (PrM p. xv). In the Theory of Knowledge (1913), he was still insisting that to understand logical terms (in particular, names of forms), we must have ‘logical experience’, that ‘those who understand [such terms as “particular”, “universal”, “relation”, “dual complex”, “predicate”] possess something which seems ﬁtly described as “acquaintance with logical objects” ’ (TK 97). (iii) Russell had no qualms concerning the existence of universals. ‘When we examine common words’, he wrote, ‘we ﬁnd that broadly speaking, proper names stand for particulars, while other substantives, adjectives, prepositions and verbs stand for universals. . . . no sentence can be made up without at least one word which denotes a universal . . . nearly all words to be found in a dictionary stand for universals’ (PP 53). Only someone in the grip of the Augustinian conception of language could take the existence of universals for granted thus. (iv) Against this background, it is not surprising to ﬁnd that Russell explained synthetic necessary truths concerning unanalysable properties in reality by reference to the natures of the entities concerned. Synthetic incompatibility, as he called colour exclusion, for example, ‘consists in the fact that two terms which are thus incompatible cannot co-exist in the same spatiotemporal place’ (PrM 233).48 (v) By the time he wrote The Problems of Philosophy, he had clariﬁed his Theory of Descriptions, and his distinction between knowledge by description and knowledge by acquaintance was in place. So we ﬁnd him asserting: ‘We must attach some meaning to the words we use, if we are to speak signiﬁcantly and not utter mere noise; and the meaning we attach to our words must be something with which we are acquainted’ (PP 32). But this does not mean that every expression stands for something with which we are acquainted. Proper names, such as ‘Julius Caesar’, obviously do not. But they are to be replaced by deﬁnite descriptions. These, duly analysed, do consist of expressions the meanings of which are entities with which we are acquainted. The guiding principle for analysis of sentences is that ‘Every proposition that we can understand must be composed wholly of constituents with which we are acquainted’ (PP 32). Prior to Russell’s encounter with Wittgenstein’s radical new ideas, he held that ‘Such words as or, not, all, some, plainly involve logical 48

A term, as Russell employed the expression at this stage, is not a linguistic expression, but the entity that a linguistic expression stands for.

The Augustinian conception of language

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notions; and since we can use such words intelligently, we must be acquainted with the logical objects involved’ (TK 99). (vi) In the Theory of Knowledge (cf. n. 39), he asserted that corresponding assertions, questions and commands all contain a common propositional component. To this extent he was committed to the view that the essential role of sentences is to describe how things are. (vii) In ‘The Philosophy of Logical Atomism’ he held that propositions are symbols, i.e. ‘something that “means” something else’ (PLAt 167). A proposition, he asserted, ‘is a complex symbol in the sense that it has parts which are also symbols. In a sentence containing several words, the several words are each symbols’ (PLAt 166). At this stage, deeply inﬂuenced by Wittgenstein’s dictations of 1913, Russell claimed that ‘The components of the fact that makes a proposition true or false, as the case may be, are the meanings of the symbols which we must understand in order to understand the proposition’, noting now that the logical connectives are an exception to this principle (PLAt 175). (viii) Russell cleaved to a Correspondence Theory of Truth. He held that ‘a belief is true when it corresponds to a certain associated complex, and false when it does not’ (PP 74). (ix) He avoided, or evaded, the paradox that he had detected in Frege’s attempt to reduce arithmetic to logic by means of the Theory of Types. But he had a persistent tendency to explain logical principles governing the use of words by reference to the nature of the entities correlated with words as their meanings (cf. (iv) above). Establishing that a word is a predicate is ﬁnding out that some property is correlated with it. ‘Exists’ is not a predicate, because what it is correlated with is not a property of objects; ‘it is essentially a property of a propositional function’ (PLAt 204). That a predicate cannot take itself as argument rests on the fact that no property of objects is also a property of properties.49 (x) Although ordinary language is endlessly misleading, inter alia because it contains a multitude of incomplete symbols, ‘In a logically perfect language the words in a proposition would correspond one by one with the components of the corresponding fact [with the exception of the logical connectives]. In a logically perfect language, there will be one word and no more for every simple object, and everything that is not simple will be expressed by a combination of words, by a combination derived, of course, from the words for simple things that enter in, one word for each simple component.’ Indeed, the language of Principia is ‘intended to be a language of that sort. It is a language which has only syntax and no vocabulary whatsoever. . . . It aims at being 49

Wittgenstein criticized Russell for appealing to the meanings of signs when establishing rules for them (TLP 3.331). Even though Russell accepted this criticism and subsequently asserted that the Theory of Types is a theory of symbols, not of things, he nevertheless continued to explain it in the same way as before.

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that sort of a language that, if you add a vocabulary, would be a logically perfect language’ (PLAt 176). Russell’s position was inherently unstable. To trace it through its various developments would be a lengthy task, which would be out of place here. But the above points sufﬁce to show that his thought was conducted within the force-ﬁeld of an array of presuppositions that is highly questionable, and that Wittgenstein challenged.

6. The Tractatus The Tractatus addressed not so much the very same problems as had been addressed by Frege and Russell, as problems that were raised by their work. Although Wittgenstein brieﬂy discussed their logicist doctrine in order to repudiate it, unlike Frege, he was not moved by the foundations crisis in mathematics. Although he touched on scepticism, it was only in order perfunctorily to repudiate it, for he did not share Russell’s preoccupation with epistemology and the attainment of absolute certainty. His primary concerns were the nature of logic and logical truth, the essential nature of representation, and the limits of language. His solutions to these problems were profoundly different from, and indeed at odds with, the doctrines of his two great predecessors. Nevertheless, his point of departure was where they had, so to speak, left the subject. Although he challenged much of their philosophy — rejecting their logicism, disproving their conception of logical propositions, and demolishing their accounts of intentionality — he nevertheless took over from them unthinkingly a variety of presuppositions. These are manifest in the ways in which his thought, like theirs, was conducted in the framework of the Augustinian conception of language and meaning. According to the Tractatus: (i) On analysis of any sentence with a sense into truth-functional combinations of elementary propositions, every constituent of such elementary propositions is a name of an object (TLP 4.22–4.221). The expression ‘object’ is here used in an extended sense (signifying a simple entity), since properties and relations count as objects too (NB 61; LWL 120), and what we ordinarily think of as objects — e.g. medium-size dry goods — are not objects at all but complexes. (ii) The object which such a simple name signiﬁes is its meaning (TLP 3.203). Objects are the sempiternal substance of all possible worlds (TLP 2.021). (iii) Objects stand in (ineffable) internal relations to each other. (As is evident from n. 26 above, in 1929 Wittgenstein explained determinate exclusion by reference to the essential natures of the objects thus related (RLF 169).) (iv) The meaning of such a simple name is correlated with the name. The correlation of a simple name in use with its meaning is psychological — it is effected by acts of meaning (see n. 16 above). In uttering a sentence ‘aRb’,

The Augustinian conception of language

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the speaker means by the sentence the state of affairs aRb the obtaining of which would make the sentence true (cf. TLP 3.11). In meaning aRb by that sentence, the speaker means by the name ‘a’ the object a that is its meaning, and by ‘R’’s being thus ﬂanked by the ordered pair of names ‘a’ and ‘b’, he means the relation of being R in which a is said to stand to b. (v) The explanation of what a simple name means is effected by an elucidation (TLP 3.263), which is a description in which the explanandum is used in a true assertion, for example, that this + is A. Such an elucidation connects a simple name with the object in reality that is its meaning. (vi) Simple names, thus connected with their meanings, are the foundations of language. (vii) The combinatorial possibilities of names reﬂect the combinatorial possibilities of the objects of which they are names. For names and their meanings necessarily share the same form. (viii) Sentences are articulated combinations of names; they are essentially complex (TLP 3.14–3.141). They say that such-and-such is thus-and-so (TLP 4.5). (ix) Names have a meaning only in the context of a sentence (TLP 3.3), not because alternative decomposition of sentences is envisaged (contrary to Frege, Wittgenstein held analysis to be unique), but because a name plays a representative role only in the context of a sentence (TLP 3.21–3.22). Only when it is a constituent of a representing fact does a name represent or go proxy for an object. In a proposition, such as ‘aRb’, it is the fact that ‘a’ stands to the left of ‘R’ and ‘b’ to its right that says that aRb (cf. TLP 3.1432). (x) The unasserted proposition is common to corresponding assertions, sentence-questions and commands (NB 96). (xi) The unasserted proposition depicts a possible state of affairs. It is a description of a possibility which the world may or may not actualize. The general propositional form is ‘Es verhält sich so und so’ (‘This is how things stand’ or ‘Thus-and-so is how things stand’ (TLP 4.5)) — the form of a description. (xii) To know what a simple name means requires acquaintance with its meaning. To use a sentence with understanding is to use the signs together with the method of projection, which is thinking the sense of the sentence (TLP 3.11), i.e. meaning by the sentence the state of affairs one is using it to depict. Understanding the utterance of another is interpreting the signs he uses as signs for the objects meant. It is acts and activities of meaning and interpreting that give dead signs life. (xiii) Thinking is a psychological process. It is a kind of language (NB 82). The constituents of thoughts are psychic entities that have the same kind of relation to things as words (CL 68). These doctrines everywhere display the framework of thought of the Augustinian conception of the essence of language. But the young Wittgenstein’s philosophy of language and logic, like Frege’s and Russell’s, was complex, subtle and anything but primitive — even though one might say of it, as one might say of theirs, that it was rooted ‘in a primitive philosophy of language’.

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So here too, there are many respects in which it deviates from various ideas rooted in the rude Augustinian conception. Not all words are names that stand for objects that are their meanings. It is the cardinal insight of the Tractatus to proclaim that the logical connectives are not representatives (TLP 4.0312). They do not stand for meanings; they are not functions at all, but operators. Likewise, formal concept-words do not have a meaning, but are in effect variables. Similarly, number-words are not names of entities. Moreover, not all sentences are descriptions. But those that are not are either senseless (like the propositions of logic) or nonsensical pseudo-propositions (like sentences of arithmetic, ethics, aesthetics and religion, as well as sentences of metaphysics, including those of the Tractatus itself ). The exceptions, in effect, prove the rule. There is no doubt that Wittgenstein himself thought that the Tractatus had been written in thrall to the Augustinian conception of language. In grappling with the problems he had inherited from Frege and Russell, he took over from them the unquestioned assumption that the basic function of words is to name things, that words which fulﬁl this function have a meaning, and that the meaning is the object represented (see Exg. §1). This will become clearer in the successive essays of this Commentary. Perhaps the most striking feature of the philosophies of Frege, Russell and the young Wittgenstein in respect of our current concern is that none of these philosophers thought that the surface grammar of natural languages conforms to the principles of the Augustinian conception of language. But all held this to be a sign of the non-transparency and/or logical deﬁciency of natural language. A logically perspicuous language or, alternatively, natural language on analysis will, in its essentials, conform to this conception. Where (if at all) it does not, very special explanation is called for — and given. In important ways, the Augustinian conception functioned for all three philosophers as a norm of representation.

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

II

Explanation 1. Training, teaching and explaining The Investigations highlights the notion of explanation of word-meaning and the associated concepts of teaching and training. Training is noted as a foundation of explanation (Z §419; PI §§5–9, 86), rule-following (PI §§143ff.) and mathematical calculation (LFM 58ff.). Reference to how words are taught and learnt is treated as an important component of concept-clariﬁcation. Practices of explaining words are studied as independent language-games (PI §28; cf. §49, PLP 94ff.), and scrutiny of different forms of explanation is a regular route for arriving at philosophical insights into the uses of words (e.g. the account of family-resemblance concepts). Wittgenstein’s strategy may be misunderstood. It may look like armchair learning-theory, long superseded by experimental psychological investigations. It may appear to introduce empirical data that are irrelevant to philosophical elucidation of meaning, conﬂating genetic investigations with concept analysis. So it may seem to be a form of psychologism. These misunderstandings miss the point of Wittgenstein’s focus upon explanation. He emphasized the internal connection of word-meaning and explanation, which is antecedent to any empirical investigations. Meaning is what is explained in giving an explanation of meaning (PG 60, 68f.). It is the correlate of understanding; and understanding is a correlate of explanation (BT 11). The meaning of an expression is not something deeper and more theoretical than what is patent in the accepted practice of explaining what an expression means; and this practice, like any normative practice, must be familiar to its participants, open to inspection, and surveyable. A caveat is necessary concerning an ambiguity in ‘explanation’. Sciences explain phenomena. But the sense of ‘explanation’ in which explanations of wordmeanings are spoken of is different from its counterpart in science (MS 109 ( Vol. V ), 108). Scientiﬁc explanations are empirical, theoretical, refutable by the facts, and revisable in the light of new discoveries. Explanations of wordmeaning, by contrast, are normative, not nomological. They are not descriptions of habits of word usage, but state rules or standards for the correct use of a word. They are not theoretical, but ground-level speciﬁcations of rules for the uses of words, just as the statement of the rules of chess are not theoretical, but describe how the game is to be played.

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Commonly Wittgenstein differentiates explanation from deﬁnition. Deﬁnition, in these contexts, is taken to be analytic deﬁnition, typically in terms of characteristic marks (Merkmale) individually necessary and jointly sufﬁcient for falling under the deﬁniendum. This is a special case of explanation. It is mistaken to suppose that the only legitimate form of explanation of meaning is deﬁnition (see ‘Family resemblance’, sect. 1). Meaning is what is given by explanations of meaning, and analytic deﬁnition has no special privileges. Wittgenstein repudiates the relevance of genetic analysis to his investigations. ‘Learning a language brings about the understanding of it. But that belongs to the past history of the reaction’ (PG 41). An explanation of the operation of language as a psychophysical mechanism is philosophically irrelevant (PG 70), for we are not interested in empirical facts (considered as empirical facts) about language (PG 66). As far as philosophy is concerned, ‘It may be all one to us whether someone has learned the language or was perhaps from birth constituted to react to sentences in German like a normal person who has learned it’ (PG 188; cf. BB 12, PI §495). Although this seems paradoxical, it is conceivable that understanding should occur without any teaching whatever. ‘Teaching as the hypothetical history of our subsequent actions (understanding, obeying, estimating length, etc.) drops out of our considerations’ (BB 14). No matter whether our current mastery of the use of an expression (or of language as a whole) was learnt, acquired as a result of a brain operation, or innate, the criteria for whether one understands the expression (a language) are unaffected. ‘The way in which language was learnt is not contained in its use’ (PG 80). Why, then, is Wittgenstein interested in teaching? ‘Am I doing child psychology?’, he queries (Z §412); ‘I am making a connection between the concept of teaching and the concept of meaning.’ There is an obvious connection. For what is taught in language-teaching is the use (the meaning) of expressions. To the extent that the teaching involves explanation and not mere training, the internal relation is evident, for not only is the object of teaching to teach the meaning, but the method of teaching is to give an explanation of the meaning. His interest in teaching ramiﬁes in various directions. (i) Teaching contexts highlight the presuppositions of a linguistic competence, as well as their contingency. Explanations of meaning given in teaching do not function in a linguistic vacuum. They are given in language. There is no extra-linguistic Archimedean point from which words or language can be explained. Language must speak for itself (PG 40). Consequently, grammatical explanations presuppose a background of prior understanding, a partial linguistic competence. With language-learners such as us, explanation has a pedagogical role only after brute training has laid the foundations of elementary linguistic skills (Z §419). Training does not involve giving reasons for doing what the learner is being trained to do. It aims to inculcate habits, dispositions and tendencies. The resultant behavioural and reactive regularities provide the basis for the possibility of teaching. Of course, the linguistic training undergone prior to teaching and explaining takes place within the framework of the natural order

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of things. It presupposes a wide range of natural human discriminatory abilities, recognitional reactions, imitative propensities and behavioural patterns. Were these different in certain imaginable ways, we would have a radically different language, or none at all. A language is part of a form of life, and the history of a language is part of the history of a culture. Examination of teaching contexts helps remind us how much is taken for granted for explanation to be possible. (ii) Explanation explains only within a language (PLP 126). A person can understand an explanation as an explanation only once he can frame questions of the form ‘What does . . . mean?’ or ‘Does he mean . . . by . . . ?’ One cannot teach a language to a child by means of explanations, and even when the rudiments of the child’s linguistic skill have been established by means of training, most of the teaching is not by means of explanations but by means of example1 and exempliﬁcation (MS 109 (Vol. V), 139; MS 114 (Vol. X) Um., 46). Explanations of meaning presuppose considerable linguistic competence in order to get a grip. They are correlates of requests for explanations of meaning. They are given in response to questions, unclarities or doubts about meaning, and they resolve misunderstandings about meaning (MS 114 Um., 44; PG 60). This is one aspect of the fact that explanations of meaning ‘belong to grammar’ (MS 114 Um., 45; PG 70). They give an array of intra-linguistic articulations rather than connecting language to reality or stating contingent truths about sounds or signs. (iii) Elementary teaching contexts often display the simpliﬁed core, the basic centres of variation, around which the complex use of an expression ramiﬁes. So it may facilitate attaining an overview of the concept. (iv) Describing the ways in which the use of a certain word might be taught is useful in destroying misconceptions (LA 1). So, for example, the diversity of parts of speech or kinds of words is highlighted in Wittgenstein’s discussion of the defects of the Augustinian conception of language. For the different ways in which one teaches names of building-elements, demonstratives, colourwords and number-words makes clear how different these linguistic tools are (PI §§8–9). Similarly, the order of teaching cannot be contrary to the order of logical priority, if any (e.g. the relation of ‘. . . is F’ and ‘. . . seems F’ (Z §§413f.), or ‘is F’ and ‘is probably F’). Further, with respect to many speciﬁc concepts, attention to features and contexts of teaching may shed light on the concept. So, for example, it is salutary to be reminded that one is not (could not be) shown a dream when one is taught to say ‘I dreamt’ (LA 2). Or that the child’s ﬁrst applications of ‘good’ are generally interjections of approval in response to food (ibid.). And it is important that the rudimentary teaching of expressions of intention would naturally introduce ‘I’m going to . . .’ as heralding an action, i.e. that when one says ‘I’m going to . . .’, one goes on to . . . (RPP I §163; see Volume 4, ‘Intending’). 1

But it is also important to note that a series of examples together with a similarity-rider is itself an explanation of meaning and a rule for the use of a word.

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(v) Focusing upon teaching highlights the purposes, and hence the standard of satisfactoriness, of explanations. We give explanations in response to such requests as ‘What does “W” mean?’ or ‘What is a W?’, and so teach the use of the word in question. We explain what a word means or what we mean by a word in order to avert a particular misunderstanding, or to establish a shared understanding of a given expression. To do so, it is neither necessary nor possible that every conceivable misuse or misunderstanding be brought to light and explicitly excluded or cleared up. A fortiori, it is not necessary to take precautions against confusions that could not occur. In giving an explanation of ‘proposition’, for example, it is not necessary thereby to distinguish propositions from cabbages. For there is no such thing as confusing a proposition with a cabbage. Hence too, pace Frege, it is no defect in an explanation of ‘number’ that it will not ‘decide for us’ whether or not Julius Caesar is a number (FA §56).2 One might object that this conception of explanation is too pragmatic. After all, when philosophers raise questions about the deﬁnition of ‘a right’ in jurisprudence, the explanation of ‘person’ in philosophy of mind, or ‘colour’ in epistemology, their questions are not guided by such pragmatic considerations. This is correct. What is doubtful, however, is whether their quest is really for an explanation of meaning simpliciter. Commonly what they need is to resolve some speciﬁc problem or puzzle, and that is furthered by attaining an overview of a concept and its place in the network of related concepts (see ‘Surveyability and surveyable representations’, sect. 3). Such an overview is not an improved explanation of the use of a word; but it enables one to disentangle the misunderstandings that led to the problem or puzzle. (vi) The examination of teaching contexts is not a form of armchair learning-theory, and its importance consists not in what it shows about learning, but what it shows about what is taught. In teaching, unlike mere training, we explain the meanings of words. Explanations of meaning are normative. They give rules for the use of words, which constitute standards of correctness that enter into the criteria of understanding (see sect. 4 below). Examining explanations of word- and sentence-meaning has three further features. (i) It illuminates what it is that we call ‘an explanation of meaning’. This has three signiﬁcant corollaries, two positive, one negative. (a) It draws our attention to the diversity of types of explanation of wordmeaning (MS 114 (Vol. X) Um., 45), e.g. analytic deﬁnition of various kinds, ostensive deﬁnition, deﬁnition by reference to samples, explanation by example, contextual deﬁnition. (b) The normativity of explanations of meaning is emphasized. For just as giving a correct explanation of what a word means is a criterion of 2

Furthermore, Wittgenstein noted, an exciting new deﬁnition of number is of no philosophical concern (MS 110 (Vol. VI), 222). For if it is new, it is not a rule that we use and that guides us in our use of number-words.

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understanding it, i.e. of knowing what it means, so too, an agreed explanation of meaning provides a standard by appeal to which members of a speech community judge correctness of use. (c) Negatively, scrutiny of our common practice of explanation of words serves as a corrective to the tendency to sublimate the notion of explanation. Truth-conditional theories of meaning take an explanation to be a rule ﬁxing the contribution an expression makes to determining the truth-conditions of any sentence in which it occurs. But this explanation of ‘explanation’ is at odds with our ordinary notion. If the meaning of ‘explanation’ is itself what is explained in our actual explanations of ‘explanation’ (of word-meanings), then such a neo-Fregean account (cf. BLA ii §56) is a distortion of our concept. It is too restrictive, failing to include much that we manifestly classify as explanation. Moreover, on this explanation of ‘explanation’, there are (as Plato and Frege held) many expressions that we constantly use correctly (e.g. ‘justice’, ‘number’), but with respect to which we cannot say what they mean or what we mean by them.3 (ii) Consideration of teaching contexts highlights what a successful explanation is. An explanation is successful if it fulﬁls the purposes of explanation in languageteaching and in clariﬁcations of meaning (PI §87(c)). It is successful to the extent that it teaches the use of an expression, averts a speciﬁed misunderstanding, or conﬁrms a shared understanding. Whether it is successful depends on the learner’s subsequent use of the expression, and on whether this use manifests understanding of the expression and hence a grasp of the explanation. (iii) Explanations may be ﬁnal, but are not immune to misinterpretation. An explanation gives a rule for the use of the expression it explains. The ﬁnality of a rule consists in there being no further rule guiding us in applying it, not in its being an infallible guide. No explanation of meaning can guarantee that there will be no misunderstandings or misapplications. But one can always add a further rule that will guide one in applying a given rule. That a rule is ﬁnal does not imply that no further rule is possible — only that in the practice of explanation, there is actually no further rule.

2. Explanation and meaning Meaning is what is given by an explanation of meaning. This reminder is important. First, it enables us to sidestep talk about meanings, with all the confusion invited by that noun. It liberates us from the illusion that ‘What does it mean?’ 3

Wittgenstein did not lack sympathy for the Platonic and Fregean vision. After all, he had once succumbed to a version of it. Nor was he, even as late as 1930, immune to its charms: ‘I struggle again and again — whether successfully I do not know — against the tendency in my own mind to set up (construct) rules in philosophy, to make suppositions (hypotheses) instead of just seeing what is there’ (MS 108 (Vol. IV), 160).

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is akin to ‘Whom do you mean?’, and that the phrase ‘to have a meaning’ signiﬁes a relation between a word and an object that is its meaning (MS 109 (Vol. V), 39). Examining what is called ‘an explanation of meaning’ will prevent us from being misled thus. For explanations are, as it were, ‘concrete’, and do not so easily mislead us, in the way ‘meaning’ does, to chase shadows (MS 116 (Vol. XII), 32f.). The dictum could be interpreted: ‘Let’s only bother about what’s called the explanation of meaning, and let’s not bother about meaning in any other sense’ (PG 69). Secondly, the dictum returns us to our ordinary linguistic practices, including our practices of explanation. Applied to the term ‘explanation’ itself, it prevents us from sublimating the notion of explanation into an arcane ideal. We have a well-established practice of explanation. This in itself lays important restrictions upon what an explanation is. (i) Explanation must be general: the grounds for an assertion, for example, must hold not only for this person and this occasion, but quite generally (PG 228). Grounds and justiﬁcations here are grammatical (not inductive) and are given in explanations. (ii) Explanations must be ‘public’, intelligible to others: There are no ‘private’ explanations. ‘If I need a justiﬁcation for using a word, it must also be one for someone else’ (PI §378). This is a distinct point from generality. It rules out, for example, the appeal to subjective perceptions (which is not ruled out by the generality requirement) as grounds for assertion. ‘I could not apply any rules to a private transition from what is seen to words. Here the rules really would hang in the air; for the institution of their use is lacking’ (PI §380). (iii) Explanations, unlike causes, come to an end. Indeed, if they did not, the purpose of explanation would be defeated. (iv) For a language to exist, there must be agreement in deﬁnitions (or, more generally, in explanations, i.e. standards of correct use), hence consensus in accepting certain types of explanation as criteria of understanding, the satisfaction of which establishes such agreement (PI §241). (v) Where explanations end lies consensual action. There is a public, agreed practice of applying explained expressions in accordance with the explanation. There are criteria determining what counts as applying an expression in accordance with its explanation and what counts as transgressing it. There is a practice of appeal to the rule given by the explanation. Thirdly, the dictum is deployed in combating the conception of language as a calculus of signs governed by strict rules that budget for all possible circumstances, and its correlate, the conception of a mental (non-conscious) or neural mechanism of understanding and interpreting. Explanations of meaning, Wittgenstein insisted, must be immanent — accessible to us and surveyable by us. Otherwise they could not fulﬁl their role as standards of correct use and clariﬁcations of what is meant. This requirement is not satisﬁed by the calculus model and is explicitly rejected by those who conceive of understanding as a hidden mechanism. But unless explanations are thus accessible, there

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would be no criteria of understanding other than correct use. Explanation would become detached from understanding (and what are ordinarily conceived as explanations would be merely heuristic). It would at least make sense to possess ineffable understanding of word-meaning, for the real, ideal explanation may not yet have been discovered, and may indeed transcend the powers of the human intellect. But, Wittgenstein insists, a meaning or sense that cannot be explained does not concern us, for one cannot act in contravention of it (MS 108 (Vol. IV), 259). Explanation is not bringing something hidden to light, merely displaying (but not making) a move in a game we constantly play.

3. Explanation and grammar That grammar is autonomous, i.e. not rendered true or correct by reference to reality, is a leitmotiv of Wittgenstein’s later work (see Volume 4, ‘The arbitrariness of of grammar and the bounds of sense’). That explanations are intra-linguistic (even though they often, as in ostensive deﬁnition, include partly concrete symbols) is an aspect of this autonomy. They belong to grammar. Giving an explanation consists in displaying appropriate connections in the web of grammar. This is evident as soon as one realizes that an explanation of the meaning of an expression is standardly intersubstitutable for the expression itself in a sentence (MS 109 (Vol. V ), 145, 248; MS 110 (Vol. VI), 19). This is patent in a deﬁnition by characteristic marks, which is clearly a substitutionrule. But it is also true of an ostensive deﬁnition, despite appearances to the contrary (see ‘Ostensive deﬁnition and its ramiﬁcations’, sect. 3). Explanations are rules. Their normativity consists in the fact that an acceptable explanation provides a standard to judge the correctness of use of an expression. This may be by way of grounds of application, legitimacy of substitution, or criteria of understanding. If meaning is what is understood when one understands an expression and what is explained in an explanation of meaning, it is evident that the idea that language contains ‘indeﬁnables’ must be re-examined. What does it mean to say that an expression is indeﬁnable (BT 256ff.)? That it is not deﬁned by specifying characteristic marks? Or that it cannot be explained? The former is unobjectionable but trivial, whereas the latter is incoherent. The requirement that deﬁnition be a kind of analysis, that it give necessary and sufﬁcient conditions for the application of an expression in the form of a conjunction of characteristic marks, is an illusory ideal that stands in the way of a correct grasp of our form of representation. First, deﬁnitions by enumeration of characteristic marks are merely one form of analytic deﬁnition. Others are prominent, e.g. in mathematics (‘prime number’) and genealogy (‘grandfather’), where necessary and sufﬁcient conditions are given by employing expressions of generality. Secondly, deﬁnition by necessary and sufﬁcient conditions is only one kind of explanation of meaning, and by no means privileged. It is important

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to note that different explanations of one and the same term may be equally legitimate. One can deﬁne an elephant by genus and differentia, but an ostensive deﬁnition at the zoo is not less correct (nor is pointing at a picture of an elephant). So, the same term may sometimes be explained in different ways. But equally, different terms may be peculiarly suited to one kind of, or a narrow range of, explanation. When this is so, this feature of the appropriate mode of explanation often reveals important facets of the type of the expression. It is no coincidence that names of perceptual qualities are explained by samples, days of the week by enumeration, prepositions by contextual paraphrase, etc. It is worth noting the diversity of types of explanation of meaning and reﬂecting on the oddity of philosophers’ insistence that deﬁnition in terms of necessary and sufﬁcient conditions is uniquely appropriate, the rest being mere approximation to this ideal. We must recognize explanations of words by reference to samples (cf. ‘Ostensive deﬁnition and its ramiﬁcations’, sects 3f.). Such deﬁnitions may involve a canonical sample (the standard metre), a standard sample (a swatch of material at the draper’s), or an optional one (any coloured object). It may involve ostension (if an observable sample is available), sampling the sample (e.g. tasting a lemon), or ‘manufacturing’ the sample (e.g. a musical note with a tuning fork). Equally it may involve locating a possible sample or giving instructions for its production. A different kind of explanation is encountered when we deal with family-resemblance terms (cf. PI §§65ff.). These we explain by means of paradigmatic examples, together with a similarityrider. The examples may vary from person to person and from time to time. If A explains a family-resemblance concept ‘F’ by reference to examples a . . . d ‘and other like cases’, and B explains ‘F’ by reference to examples e . . . h ‘and other like cases’, it does not follow that their understanding of ‘F’ differs as long as citing a . . . d and citing e . . . h are both criteria for understanding ‘F’ and so acknowledged in the general practice of explaining ‘F’. There are many other types of equally legitimate explanation: locative explanations, contextual paraphrase, contrastive paraphrase, explanation by enumeration, explanation by examples together with a generative rule, etc. One reason for the failure to take seriously different kinds of explanation is a misconception about adequacy. Such a misconception is evident in the Fregean idea that an explanation of a concept is complete if and only if it unambiguously determines of any object whether or not it falls under the concept. Similarly, an explanation is held to be successful if and only if it enables the hearer to decide of any object whether or not it falls under the concept (given the facts). Judged by these standards of adequacy, most actual explanations, indeed many kinds of explanation, are defective, i.e. neither complete nor successful. But, as Wittgenstein emphasizes, an explanation is adequate if it fulﬁls its purpose (PI §87). Correctness differs both from completeness and from success. Success is an external pedagogical property of explanations. A has successfully explained to

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B what ‘F’ means to the extent that his explanation enables B to go on and make at least those applications of ‘F’ which, in the practice of the language, are justiﬁed by reference to that explanation. Correctness and completeness, by contrast, are internal normative properties of explanations. An explanation may be correct but incomplete. It is perfectly correct to say that justice (or, perhaps more accurately, dikaiosun¯e ) is, inter alia, paying one’s debts. Socrates is wrong to reject this explanation altogether; rather, he should point out its limitations, remind us that justice also takes other forms (cf. MS 114 (Vol. IX) Um., 108; BT 69). We may call this feature ‘incompleteness’, but it does not consist in the fact that the explanation will not decide for us whether the number two is just. Rather, it consists in the fact that there are legitimate standard applications of the term which we do not take to be warranted by this explanation. One could not justify the application of ‘just’ or ‘unjust’ to strict liability in the penal code by reference to Cephalus’s explanation. Giving a correct explanation is a criterion of understanding, whereas failing to give a complete explanation is not a criterion for failing to understand. Indeed, in many circumstances, giving a correct but incomplete explanation is a criterion of understanding, or, at least, of partial understanding. Only if Cephalus were to give an incorrect explanation of ‘just’ or were to misuse it, would there be grounds for Socrates to deny that he understands it. What, then, is a complete explanation? Clarifying this involves noting three features of the general idea of completeness. (i) ‘Complete’ and ‘incomplete’ are correlative terms. It only makes sense to say of something that it is incomplete if it makes sense to say that it is complete; i.e. we can intelligibly speak of an incomplete so-and-so only if we can specify what would count as a complete one. (ii) ‘Complete’ and ‘incomplete’ are relative terms. There is no absolute standard of completeness. Rather, what counts as a complete so-and-so depends upon what the so-and-so is, and what criteria (if any) we ﬁx for a complete one. (iii) Incompleteness is in general a defect relative to the purposes by reference to which particular criteria of completeness are ﬁxed. Note the parallels with the concepts simple/complex and exact/inexact. In particular, incompleteness, like inexactness, is in general a relative defect, but neither feature is uniformly so. An incomplete or inexact so-and-so may sometimes suit our purposes perfectly. How does this bear on the idea of completeness of explanation? A complete explanation of an expression is an explanation that may legitimately be invoked as a standard of correctness for the application of that expression in normal contexts. Relative to this standard of completeness, explanations may be incomplete in failing to provide a sufﬁciently general standard of correct use. An incomplete explanation may be perfectly adequate in certain contexts, e.g. when only one aspect of an expression is in view, or when establishing a roughand-ready understanding sufﬁces for the purposes at hand. The completeness of an explanation of meaning is not (contra Frege) a logical or formal feature of the explanation (e.g. laying down necessary and sufﬁcient conditions of

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application). It is, rather, a feature of the normative role of the explanation in the practice of using the expression, and of the role which giving that explanation has in establishing understanding. Thus, for example, an ostensive deﬁnition of ‘red’ is not incomplete because it provides no application rule or because it fails to explain secondary uses such as ‘He saw red and lashed out in fury’. And an explanation of a family-resemblance term by paradigmatic examples may be deemed complete, even though its rider ‘and other like things’ leaves the boundary of the concept open. Most speakers, one might think, can give only incomplete explanations of the meaning of words they use and understand. It is the task of lexicographers to discover or assemble the complete explanations. This is misleading. For a comprehensive synopsis of different explanations of divergent uses of an expression is not a more general (hence complete) explanation of any particular use. The lexicographer’s concatenation of explanations is not a unitary explanation that serves as a standard of correct use for every application of its explanandum. Giving a correct explanation (or even a complete one, in cases where there is one) does not guarantee understanding. The learner must in addition grasp the method of projection of the explanation. Pointing at a scarlet rose and saying ‘That colour is red’ will not delineate the boundaries of the concept of red. ‘Only the application of language can show how it is to be applied’ (MS 110 (Vol. VI), 70). The learner must learn the application from our practice (and even if we had a supplementary rule here, he would still have to learn how to apply it — from our practice). Consequently, giving a correct explanation is only a criterion (defeasible evidence) of understanding, not a sufﬁcient condition of understanding. For if a person has failed to grasp the (internal) relation between explanation and application, i.e. what counts as a correct application of the rule given by the explanation, then he may give a correct explanation of ‘W’, and yet regularly misapply the word in some standard context. There can be more than one complete explanation of an expression, even in a single context. Pointing at scarlet or at maroon objects in explanation of ‘red’ gives equally correct and complete ostensive explanations of ‘red’; cricket, chess and tiddly-winks, or rugger, draughts and poker are equally good examples in a family-resemblance explanation of ‘game’. What the different complete explanations of the same expression share is a common status in the practice of explanation. Giving any correct explanation is a criterion of understanding, and if it is complete, it can equally be appealed to as a standard of correctness of use in all normal cases. Must every signiﬁcant expression in a language have a complete explanation? There seem to be numerous counter-examples to this suggestion. Ramiﬁed psychological concepts such as thinking, believing or understanding constitute, as it were, one end of a spectrum of such cases. Applicatives, prepositions and many adjuncts, disjuncts and conjuncts constitute the other. In the latter kinds of case, we manifest our understanding by contextual paraphrastic explanation.

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There is no explanation of the meaning of ‘on’ simpliciter, yet it makes a signiﬁcant contribution to phrases and sentences in which it occurs. If asked for the meaning of such words, we typically respond by asking for the context of their occurrence (e.g. ‘on the table’, ‘on the agenda’, ‘on the air’, ‘on call’, ‘on further reﬂection’, ‘on Monday’). But this does not show that our understanding outstrips our ability to explain what we mean and what the words we use mean in the context of our utterances. The fact of the matter is that we can and do explain the various phrases to which these prepositions, etc. contribute. There is (and surely need be) no explanation which fulﬁls the role of standard of correct use for an expression of the kind in question in all standard contexts. On the one hand, they clearly make a non-trivial contribution to contexts in which they occur (which we can readily explain); on the other, there is no general explanation of what they mean (not even by way of a general rule specifying their systematic effect on the context of their occurrence). But there is nothing here that we do not know, nothing that awaits discovery that might disclose to us what our expressions really mean.

4. Explanation and understanding The concept of understanding and its relationship to meaning and explanation are prominent in Wittgenstein’s philosophy of language. Is he therefore guilty of not separating the psychological from the logical? Such an accusation rests on a misunderstanding of what is wrong with psychologism. Frege’s repudiation of psychologism rested on the insight that meaning (sense) is objective, public and communicable. Ideas, which were, for the ‘psychological logicians’, the gold-backing for the currency of words, were conceived to be identiﬁabilitydependent on their owners, privately owned and epistemically private. This, Frege held, excludes them from playing any role in logic or the communication of thoughts by means of language. This confused4 criticism of empiricist misconceptions, however, does not imply that understanding is irrelevant to a correct account of meaning. Since the meaning of a word is what is grasped when someone knows its meaning (i.e. can answer the question ‘What does it mean?’), the concept of understanding is pertinent to our investigation. While the psychological accompaniments of understanding are irrelevant, the criteria of understanding are not. They show the grounds for ascribing understanding to a person, for attributing to him a grasp of the meaning of a given expression. Hence the concept of understanding gives us leverage upon that of meaning. The criteria 4

Confused, since ideas are not identiﬁability-dependent upon those who have them. A and B may have exactly the same idea, not merely qualitatively identical but numerically distinct ones, for the distinction between numerical and qualitative identity does not apply to ideas. Moreover, the person who has an idea does not own it — having an idea is not a relation between a thinking subject and an idea.

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of understanding are perfectly public, and the object of understanding is perfectly communicable. So invoking understanding in a philosophical clariﬁcation of meaning need involve no psychologistic commitments. But the concept of understanding must ﬁrst be clariﬁed on pain of further confusions in the investigation of meaning. Explanation is internally related to understanding. But not everything that brings about understanding is an explanation. If we had a drug which had the effect of producing knowledge of French in its taker, taking the drug would not be a kind of explaining, nor giving it a kind of teaching (B i §34; PLP 126). Explanation gives the content of understanding. Hence explanation would still be necessary to specify what is understood even if the understanding were innate or induced by drugs. To understand an expression is to know what it means. But if one knows what a given expression means, must one be able to say what it means, i.e. answer the question ‘What does it mean?’? By deﬁnition, a competent speaker uses his language correctly. But may not his ability to use language outstrip his ability to explain that use? And if he can give explanations of a sort, may they not merely point out, hint at, show, the path towards correct use or proper explanation, and hence be ‘scientiﬁcally speaking’ inadequate? This was Frege’s view, and is still widespread. If the concept of explanation is sublimated, then there is indeed no reason why explanation should be the correlate of understanding: ‘Often it is only after immense intellectual effort, which may have continued over centuries, that humanity at last succeeds in achieving knowledge of a concept in its pure form, in stripping off the irrelevant accretions which veil it from the eyes of the mind’ (FA p. vii). And when we come to ‘indeﬁnables’, the best we can do, in Frege’s view, is ‘to lead the reader or hearer by means of hints, to understand the words as intended’ (CO 193). Wittgenstein disagreed. What an expression means cannot be something hidden from the view of competent users of the expression. ‘Can only logical analysis explain what we mean by the propositions of ordinary language? Moore is inclined to think so. Are people therefore ignorant of what they mean when they say “Today the sky is clearer than yesterday”? Do we have to wait for logical analysis here? What a hellish idea!’ (WWK 129f.). We did not need to wait upon Frege’s deﬁnitions of ‘nought’, ‘one’, ‘two’, etc. in order to know what they mean. Pointing at a pair of nuts on the table and saying ‘That is called “two” ’ is a perfectly correct explanation of what ‘two’ means (PI §28). Explanations of the meanings of words are not discoveries. There are no such things as ineffable meanings, even if no deﬁnitions are available. A competent speaker understands the expressions of his language, knows how to use them, can say what he means by their use from context to context. What are the criteria of his understanding? Wittgenstein emphasizes three: correct use of the expression, i.e. use in accordance with the general practice; giving correct explanations of use, i.e. explanations of what the expression as used in a given context means; and responding appropriately to the use of the expression.

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The ﬁrst two are related in the following way. To know what ‘W’ means is to be able to answer the question ‘What does “W” mean?’. If a person understands an expression, then he knows what it means, and if he knows what it means, then he can, standardly, answer the question ‘What does it mean?’, i.e. explain what it means. A competent speaker who uses ‘W’ correctly can explain its use, minimally, simply by invoking examples of its use. Many words can be explained perfectly well by spelling out appropriate examples of their applications (TS 211, 514; PG 119f.). Examples are not a kind of hocus-pocus, nor are they mere hints at explanations (PG 273). Equally, if an appropriate instance is available, someone can use it as a sample to give an ostensive deﬁnition. For if he is able to say of the red object that it is red, then he is also in a position to explain what ‘red’ means by saying of the colour of that object that it is red. Such an ostensive deﬁnition is not an ‘aid’ to understanding, but is a rule, belonging to the symbolism, for the use of the word deﬁned (MS 110 (Vol. VI), 213). Further, if no sample is available, but a person knows where one is, he can give a locative explanation; and so on. These connections between ability to use and ability to explain depend upon a humdrum interpretation of what counts as an admissible explanation. Though correct use and correct explanation are thus connected, they do not entail each other. It does not follow from the fact that someone has used ‘W’ correctly in a given sentence that he will, on demand, explain it correctly. He may explain it incorrectly, thus casting doubt upon his understanding of ‘W’. Yet normally, if he uses a word correctly in typical contexts, he will also explain it correctly. Similarly, a person may give a correct explanation of a word, and if he does, he will normally also use it correctly. If he explains ‘circle’ as ‘a plane ﬁgure each point of which is equidistant from a given point’, or as ‘the shape of a ten-penny piece’, or as ‘that ﬁgure over there’, he will normally use the term ‘circle’ correctly in sentences such as ‘The circle over there is too small’, or ‘Can you draw a circle here?’. But he may not know how to apply the rule he has given in his explanation in the correct (accepted) way. He may give a correct ostensive deﬁnition of ‘violet’, but go on to call indigo objects ‘violet’. He may use ‘yellow’ as we use ‘something yellow’, and hence give the same ostensive deﬁnition as we do, but use the expression deﬁned differently (MS 116 (Vol. XII), 118). Then his incorrect use will defeat the support given by his correct explanation to the assertion that he understands the word. Indeed, it will manifest his not actually understanding the explanation, since he misapplies it. However, these two criteria normally converge. Can there be a gap between a person’s understanding and his ability to explain what it is that he understands, between his knowing what a word means and his being able to say what it means. We must admit the possibility of defective explanations, e.g. by giving poor examples in explaining a familyresemblance concept or borderline paradigms in ostensive deﬁnition. Equally, one must budget for common forgetfulness or lack of linguistic self-consciousness, e.g., leaving a very important aspect of use unmentioned (similar to explaining

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the moves of the chess king, but forgetting the castling rule). So, it would be common to explain ‘nearly’ as having much the same meaning as ‘almost’, quite forgetting their uses after negation. Few of us could readily pinpoint the difference in meaning, in use, between ‘small’ and ‘little’ (‘small change’, but ‘a pathetic little smile’) or between ‘shut’ and ‘close’. Does it then follow that we sometimes know what a given word means, but cannot explain its use? Or that we know what we mean by what we say (in uttering a sentence containing ‘W’) but cannot explain what we mean? But then what does knowing what ‘W’ means consist in? We are imposing the wrong picture. The internal relations between understanding, meaning and explanation do not require of a person who understands an expression that he be able to give an overview of its use, only that if he has used an expression on a given occasion and cannot explain what it means in that context of use, then he does not understand what he said or, other things being equal, what the expression thus used means. The following points should be noted. First, it is our giving a correct explanation that is a criterion of understanding, and this need not be a synopsis of use, let alone a synopsis of comparative uses. Most of us would be stumped to answer the question ‘What does “at” mean?’, and would characteristically respond, ‘In what context?’, or ‘What particular phrase do you have in mind?’. We may not be able to give a synopsis of use, but it does not follow that we cannot explain. No competent speaker would normally have any difﬁculty in giving a paraphrastic explanation of ‘at 2.00’, ‘at the cross-road’, ‘at school’, ‘aimed at the bird’, ‘alarmed at the commotion’, ‘left it at that’, etc. It is these latter exercises that constitute criteria for understanding. Further, while it is mistaken to say that ‘almost’ has exactly the same meaning as ‘nearly’, the criteria of understanding are perfectly satisﬁed if someone, asked what ‘they have nearly ﬁnished’ means, answers that it means the same as ‘they have almost ﬁnished’. Giving this explanation does show that he understands perfectly well what the sentence means. Secondly, in order to satisfy the criteria for understanding what ‘W’ means, it is not necessary that one be able, without more ado, to explain how it differs in meaning from its cousin ‘V’. One may not have thought of the fact that ‘not nearly’ cannot be replaced by ‘not almost’, but were someone to say ‘That is not almost enough?’, one would query whether they meant that that was not nearly enough. This already shows that one is perfectly aware that they are not everywhere intersubstitutable, and can spot cases of misuse perfectly adequately. Thirdly, we must consider what are the criteria for a person’s being able, or not being able, to give a certain explanation. Clearly, the mere fact of not giving a particular explanation does not establish inability to give it. If a person is stumped for a reply to a request for an explanation, and we suggest one to him, and he sincerely responds, ‘Oh yes, of course; I should have thought of that’ — we would frequently be willing to claim that he would have been

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able to explain if. . . . We will normally be satisﬁed with his acknowledging the correctness of correct explanations. Fourthly, we must recall the large variety of generally acceptable explanations. That a person cannot explain ‘circle’ as ‘the locus of points in a plane equidistant from a given point’ does not show that he cannot explain what ‘circle’ means, and does not support the contention that such a person’s understanding (ability to use) outstrips his ability to explain. If he points at a circular ﬁgure and says ‘That + [shape] is a circle’, he has explained the term — although not for the purposes a geometrician may have in view. Finally, one source of the idea of knowing but not being able to say is the traditional idea that some words name ‘simple ideas’ or ‘indeﬁnables’. Everyone knows, one might think, what ‘red’ means — but no one can say. Does one depend here upon an elucidation ‘relying upon an understanding willing to meet one half-way’? That Fregean idea rests on too restrictive a conception of explaining. Ostensive deﬁnition by reference to a sample says what red is, explains what ‘red’ means. The sample together with the deictic gesture and demonstrative is a symbol. Similarly, understanding of a familyresemblance concept is not ineffable. We do know what ‘justice’ means or what games are, and we know how to say these things too, not by ‘essentialist’ analytic deﬁnitions, but by explanations by examples together with similarityriders (see ‘Family resemblance’). These do say what ‘game’ or ‘justice’ mean. We need have no qualms about meanings being ineffable or understanding being opaque.

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

III

The language-game method 1. The emergence of the game analogy The picture of ordinary language adumbrated in the Tractatus is of a deceptive surface grammar concealing the true logical forms of logical grammar. Natural languages, contrary to what Frege1 and Russell2 had held, are in good logical order. For nothing can be said, nothing can be represented in a language, without the language being in good logical order. For there are no degrees of sense. A sentence can no more make a little bit of sense than a child can be a little bit illegitimate. So whenever propositional signs are used to say something, whenever they are ‘thought’ and applied in describing how things are, then a sense is expressed. And if any sense is expressed then it must be determinate (an indeterminate sense, it seemed, was no better than no sense at all). Underneath the superﬁcial forms of natural languages is a sharp and rigid calculus, which is mapped on to the forms of surface grammar by a multitude of conventions of which speakers are not even aware (TLP 4.002). The hidden calculus of language is determined by the rules of logical syntax, which constitute the depth grammar of any possible language. Such rules specify the combinatorial possibilities of the members of the various categories of simple names that are the constituents of elementary propositions. Further rules govern the generation of molecular propositions from the array of elementary ones, and further conventions determine the surface forms in which such propositions appear in natural language. The calculus conception began to disintegrate over the problem of colour exclusion. For the linchpin of the logic of the Tractatus had been the independence of the elementary proposition (i.e. that any elementary proposition can be true or false and everything else remain the same). On that assumption rested the account of logic. For the whole of logic was supposed to follow from the mere idea of the elementary proposition as such. If that idea is given, then so too are the notions of truth and falsehood. If they are given, so too is the idea of negation. With the mere idea of successive assertion, the idea of conjunction is given, and if negation and conjunction are given, so is the N-operator ( joint 1

See Frege, Begriffsschrift, Preface; PW 6f., 143, 266, 270; PMC 67f., 71. See Russell, ‘The Philosophy of Logical Atomism’, repr. in The Collected Papers of Bertrand Russell, vol. 8 (Allen and Unwin, London, 1986), p. 176; also his ‘Introduction’ to TLP, p. x.

2

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negation). Hence, all possible truth-functional combinations of any set of elementary propositions are given. And hence too, if all elementary propositions are given, all the propositions of logic are given. But with the realization that logical relations can be determined by the content of elementary propositions, and not just by their truth-functional combinations, the Tractatus conception of logic and of its topic-neutrality required reconsideration. Wittgenstein’s ﬁrst move, evident in ‘Some Remarks on Logical Form’ and in Philosophical Remarks, chapter VIII, was to introduce the idea of a propositional system (Satzsystem). This was intended to shore up the conception of language as a calculus, not to ditch it. Propositions ascribing determinates of a given determinable were conceived to belong to systems, i.e. sets of propositions between the members of which relations of exclusion obtain which are not consequences of truth-functional combination, but of the concept-words occurring within the propositions. For such systems, the truth-tables for the logical connectives had to be rewritten to exclude the simultaneous truth of, for example, ‘A is red’ and ‘A is green’, and to take into account that from ‘A is red’ it follows that ‘A is not green’ (or blue, or yellow, etc.). But it became progressively clearer that the price to be paid for this in terms of ramifying complexity was excessive.3 Moreover, the range of application of the idea of a propositional system was narrow (namely, determinates of a determinable). Even within its range, the mere rewriting of the rules for the connectives and quantiﬁers failed to capture more than a fragment of the grammar of the concepts in question. For budgeting for colour exclusion in the Satzsystem of colour predicates said nothing about the further grammatical articulations between ‘being red’ and ‘seeing red’, between ‘I see a red A’ and ‘He sees a red A’, between ‘is red’ and ‘looks red’, between ‘looks red to me’ and ‘looks red to him’, etc. Furthermore, other elements of the Tractatus structure began to crumble too — the ontology collapsed, and with it the whole idea of a ‘connection between language and reality’ (see ‘Ostensive deﬁnition and its ramiﬁcations’, sects 1 and 3). Hence too the picture theory and its account of the intentionality of thought and proposition, which depended on there being such connections, crumbled (see Volume 4, ‘Intentionality’, sects 2–4). The analogy between the calculus of language and the calculus of chess played no part in Wittgenstein’s early reﬂections on language. But on his return to philosophy, it came to preoccupy him, initially in relation to the controversy between Frege and the formalists. Heine and Thomae (quoted by Frege, BLA ii §88), and later Weyl (WWK 103), argued that arithmetic is a game with contentless signs played according to combinatorial rules. Numerals are akin to chess pieces; both are merely external signs for, foci of, a set of rules. 3 As indeed Russell noted on reading Philosophical Remarks: ‘His theories are certainly important and certainly very original. Whether they are true, I do not know; I devoutly hope they are not, as they make mathematics and logic almost incredibly difﬁcult.’ Letter from Russell to Moore 5 May 1930, in The Autobiography of Bertrand Russell, vol. 2 (Allen and Unwin, London, 1968), p. 198.

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In June 1930 and on later occasions, Wittgenstein discussed the formalists’ conception of arithmetic, their use of the chess analogy and Frege’s reactions to it (WWK 103–5, 124, 150f., 163, 170). Frege presented two alternatives: either mathematics is about signs, ink marks on paper, or it is about what those signs represent, namely numbers. But, Wittgenstein objected, this is a false dichotomy. This he clariﬁed by the formalists’ chess analogy. A game of chess is not ‘about’ chess pieces (if the queen is carved so as to appear ﬁerce, she will not be any more powerful in the game). But the pieces do not go proxy for anything. One could really say that the ‘meaning’ of a chess piece is the sum of rules that determine its possible movements. But equally correctly, that it has no meaning. Similarly, Frege is right that the sign ‘0’ does not have the property that when added to the sign ‘1’ it yields the sign ‘1’, but wrong to infer that ‘0 + 1 = 1’ is therefore ‘about’ numbers.4 The chess analogy suggests an alternative conception: namely, that numerals used in sentences of pure arithmetic have no meanings. Only the applications of arithmetic give it any meaning. The sentences of pure arithmetic are in effect rules. They govern the use of numerals in transformations of sentences of applied arithmetic. Wittgenstein utilized the analogy more extensively than did the formalists. If language is conceived as a logico-syntactical calculus, the analogy with chess can highlight important features. (i) The rules of chess have no foundations and cannot be justiﬁed by reference to reality. They are autonomous; nothing, other than our decisions, dictates them.5 Similarly, he now held, the rules of language have no foundations. Nor are they ineffably necessitated, as a condition of the possibility of representation, by the alleged forms of the world. (ii) The rules of chess, not being answerable to any reality, could be different. But if you change the rules, you change the game. ‘Losing Chess’ is a different game from chess. So too, the rules of language are, in the requisite sense, arbitrary (see Volume 4, ‘The arbitrariness of grammar and the bounds of sense’). They too could be different. But then the words would mean something else.6 (iii) The rules of chess are constitutive of the game. They are to be distinguished from the strategic rules that tell one how best to move one’s pieces Wittgenstein was later to express much the same point in asserting that ‘3 + 3 = 6’ is not about the number 3, but if one wants a proposition that could be said to be about the number 3, then ‘There are three people sitting on the sofa’ is as good a candidate as any. 5 In MS 113 (Vol. IX), 117r, Wittgenstein remarks that Frege would have said that there could be people who are acquainted only with the ﬁrst ﬁve cardinal numbers, but the rest of the series exists irrespective of their, or our, knowledge. Does chess also exist independently of us? See also TS 219, 8: the analogy with chess illustrates the autonomy of language, for it diminishes the temptation to conceive of meaning as an object which can be pointed at. 6 To be sure, one needs to distinguish essential from inessential rules, as Wittgenstein noted (PI §562; see Exg.). Changes of the rules that, in our judgement, do not affect essential features of the game (or of the use of a word) do not imply that we are now playing a different game (or that the word now means something different). 4

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in order to win. Similarly, the rules of grammar (in Wittgenstein’s idiosyncratic use of the term) determine what makes sense, not what is true or what will be useful to say. They are constitutive of the meanings of expressions. (iv) The rules of chess determine the possible moves of a chess piece. Similarly, the logical syntax of a word determines its place in grammar, its logico-syntactical combinatorial possibilities. All that is lacking is the assignment of meaning, i.e., a method of application. (v) It is the method of application that differentiates language (and applied mathematics) from chess (and pure mathematics).7 There are analogies between the calculus of chess and a language, but they must not overshadow the dissimilarities between a calculus and a language. The importance of these differences only gradually became clear to Wittgenstein in the 1930s. A provisional list of some of the misleading features of the calculus conception may be helpful at this stage (more detailed examination will be provided elsewhere). (i) Being derived from the calculi of mathematics and logic, the calculus conception implies that a language is governed by a system of computable rules, and that in speaking a language we are operating such a computational system. It may also appear to imply a system of rules covering all possible cases, whereas our language does not (and could not) lay down rules which will dictate a result for every conceivable circumstance (see Exg. §§80, 84–7). (ii) It suggests a system in which there are primitive and derived terms, the derived terms being deﬁned in terms of the primitives, and the primitive terms having a completely sharp, unitary meaning. This in turn fosters a misconception of explanation, of the diversity of forms of explanation (see ‘Explanation’), and of ostensive deﬁnition as providing the foundations of language by linking indeﬁnables to reality (see ‘Ostensive deﬁnition and its ramiﬁcations’). (iii) It obscures philosophical problems concerning a rule-formulation, the rule it expresses, and the practice of applying the rule. This subject is the focal point of Wittgenstein’s discussions of following rules in the Investigations (see Volume 2, ‘Following rules, mastery of techniques and practices’). (iv) The calculus conception of language (e.g. in Frege or the Tractatus) misconstrues the principle that a word has meaning only in the context of a sentence. (Frege gave this principle a function-theoretic justiﬁcation; the Tractatus gave it a picture-theoretic justiﬁcation; both were misguided (see ‘Contextual dicta and contextual principles’, sects 1–3). (v) Hence too, it distorts the nature of understanding. It can readily seem as if understanding the speech of another is assigning to his words the same interpretation as he has. Then it appears as if understanding what he meant is calculating or computing the meaning of a heard sentence from the meanings 7

The sting lay hidden in the last two points. When Wittgenstein turned to undermine the calculus conception of language, the misconceptions implicit in them were clariﬁed.

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of its constituents and the manner of their combination. But understanding is not such a process (cf. ‘Understanding and ability’, sects 4–6), and not all understanding could be interpreting (see Exg. §§198–201). (vi) It idealizes syntax by encouraging the myth of ‘logical form’ that will be displayed perspicuously by ‘logical syntax’ and will provide a univocal method of distinguishing sense from nonsense. But use and diversity of use are not mirrored in form, neither in the grammatical forms of natural languages nor in the forms of the invented calculi of logic. And nonsense is often contextdependent (see Volume 4, ‘The arbitrariness of grammar and the bounds of sense’, sect. 5). (vii) It is not readily adaptable to the fact that radically different explanations are often equally correct for one and the same univocal expression, and it tends to obscure the diversity of types of expression (see ‘Explanation’). (viii) It opens up, at least potentially, a gap between the internal relations set up within the calculus (the intra-calculus explanations) and the commonor-garden explanations that we accept in our linguistic practices as criteria of understanding. Consequently, it raises a problem of ‘ﬁt’. Given a model calculus of a language, what features will show it to be correct? If the intracalculus explanations of meaning diverge from our ordinary explanations of meaning, what independent data can vindicate the model? These considerations (and others) led to the progressive erosion of the calculus conception of language. But, as it crumbled, the chess analogy was not abandoned. For as the analogy between a language and a game became more prominent in Wittgenstein’s reﬂections in the early Thirties, chess continued to provide a fruitful object for comparison, not because it is a calculus, but because it is a game. Wittgenstein’s attention shifted from the geometry of calculi to the integration of rule-governed symbolisms into human practices. It appears to have been in 1931 that the analogy between speaking and playing a game, and between the rules of a language and the rules of a game began to preoccupy Wittgenstein. The thought that in speaking a language we might not be following strict rules on the model of a calculus seems to have occurred to him in the context of reﬂections on the use of general concept-words (e.g. ‘leaf ’) and of proper names (e.g. ‘Moses’). Having reﬂected on the ﬂuid ‘meaning’ of proper names (in an antecedent of PI §79; see Exg.), Wittgenstein noted that it is perfectly possible to describe a calculus exactly with the sole purpose of thereby characterizing a whole group of other calculi. So one might describe draughts in detail simply in order to explain what a board game is. He continued thus: Wasn’t it a mistake of mine (for so it now seems to me) to suppose that someone who uses language always plays a particular game? For wasn’t this the point of my remark that everything about a proposition — no matter how vaguely it may be (expressed) — ‘is in order’? But didn’t I want to say: everything must be in order if someone utters a sentence and applies it (or, what comes to the same thing, reads it off a fact)?

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But there is nothing in order or out of order about this, — it would be in order if one could say: this man too is playing a game in accordance with a particular ﬁxed — speciﬁable — list of rules. (MS 112 (Vol. VIII), 95r)

But this is just what we do not ﬁnd in the case of the use of ordinary proper names, he continued. For here there are no strict rules. There is, rather, a ﬂuid use. Does not the analogy of language with a game open our eyes? We can, after all, easily imagine people amusing themselves in a ﬁeld by playing with a ball in such a way that they successively begin various existing games without ﬁnishing any, and in between perhaps throw the ball aimlessly, pick it up, let it drop, etc. Suppose someone says: the whole time they are playing a ball-game and are following deﬁnite rules at every throw. — But — it will be objected — the person who said ‘N is dead’ didn’t string words together aimlessly (and that’s what his ‘meaning something by his words’ consists in). — But one can indeed say that he uttered the sentence aimlessly, which is shown by the [previously] described uncertainty [in specifying whom he meant by ‘N’]. Of course, the sentence didn’t come out of the blue, and, if you like [you can say that], he too is playing a game with very primitive rules. For it is perfectly true that to the question ‘Who is N?’ I got an answer, or a whole series of answers, that were not completely irregular. — We can say: let’s investigate language in respect of its rules. If here and there it has no rules, then that is the result of our investigation. (MS 112 (Vol. VIII), 95v–96r = BT 254; an ancestor of PI §83)

It rapidly became clear that the conception of language as a calculus was defective. It needed to be replaced by something much looser and more ﬂexible — something like the activity of playing a game, loosely governed by rules that do not try (absurdly) to budget for all conceivable eventualities. If anyone objects to saying that the rules of grammar are rules of games, he is right in the sense that what makes a game into a game, the competition of the players, the purpose of entertainment and relaxation, is absent from grammar, etc. But no one will deny that the study of the nature of rules of games must be useful for the study of grammatical rules, since some sort of similarity undeniably obtains. It is on the whole better to reﬂect on rules of games without any ﬁxed opinion or prejudice about the analogy between grammar and game, but merely to be driven by the sure instinct that there is here a kinship. And here again one should simply report what one sees, and not fear that one is thereby undermining an important aspect, or that one is wasting one’s time on something irrelevant. One sees then above all how the concept of a game and with it that of rules of a game are blurred at the edges. (MS 113 (Vol. IX), 30v; cf. MS 114 (Vol. X) Um., 161)

Wittgenstein was attracted not only by the analogies between language and speaking, on the one hand, and games and the playing of games, on the other, but also by the fact that, in his view the concepts of language and of a game

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have signiﬁcant common features. The concept of a game became his favoured example of a family-resemblance concept (see ‘Family resemblance’). Games exemplify the important features of family resemblance, which, he thought, also characterize language, proposition and rule, which were at the centre of his concerns. The concept of a game is not speciﬁed by a list of necessary and sufﬁcient conditions. Rather, it is characteristically explained (and can perfectly well be explained) by reference to a series of examples and a similarity-rider. Games, in all their variety, form a family, united by numerous overlapping similarities, rather than by a set of characteristic marks shared by all games. So too, he thought, the concept of language is a family-resemblance concept. When Wittgenstein wrote the Tractatus, he thought that a language is deﬁned as a totality of propositions (all sharing a common propositional form) that can be produced from a given fund of elementary propositions by the Noperator. Now he repudiates the whole conception of a general propositional form, and emphasizes that the concept of a proposition is a family-resemblance concept, that incorporates within its extension propositions of numerous logically different kinds — e.g. observational propositions; closed and open generalizations; hypotheses; scientiﬁc hypotheses; theoretical propositions in science; avowals of experience, thought or intention; third-person psychological propositions; propositions of ethics, aesthetics or religion; mathematical propositions, logical propositions. What unites the members of the family of propositions is not a common essence, but overlapping similarities. Similarly, the concept of language is a family-resemblance concept. A language is a motley of language-games, which cannot be circumscribed in advance of the facts, and which lends itself to indeﬁnite expansion. Wittgenstein had once thought that such concepts as proposition, truth, logical operation, truthfunction, were ‘metalogical’, i.e. concepts that perforce characterize anything that can be called ‘a language’, and that picturing and hence describing were of the essence of any possible language. But this, he now realized, is quite wrong. No special primacy attaches to the declarative sentence or to the assertoric speech-function (and hence no special primacy to the notion of truth and truth-condition). For we can imagine a language consisting only of commands (e.g. the language-games of §2 and §8), or only of sentence-questions and yes/no answers (PI §19). So too, no special primacy attaches to description (see ‘Descriptions and the uses of sentences’) — for commands in such an imaginary language-game cannot be deemed descriptions. Rudimentary languages such as these (and, indeed, much more evolved ones too) involve no truth-functional combinatorial devices, but they are recognizably languages for all that. One cannot say how many different language-games must coexist to constitute a language, and, to be sure, Wittgenstein thought that the requirements are minimal (vide language-game (2)). But even if we think that language-game (2) is insufﬁcient to constitute a language, it is surely correct that there is no hard and fast line separating what is from what is not a language.

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The analogy between a game and a language did indeed prove illuminating. Games, like languages, are creations of human beings in their social interactions. They are not answerable to reality for correctness. They are, by and large, rule-governed. The rules of a game are constitutive rules, as are rules of grammar. Unlike those of a calculus (but like the rules of language), they are not ‘closed’; they do not attempt to budget for all eventualities. But they are not therefore deemed incomplete. ‘Grammar describes the use of words in the language. So it has somewhat the same relation to the language as the description of a game, the rules of a game, have to the game’ (PG 60). The foundation of the ability to play a game, like the foundations of our linguistic skills, typically lies in training. The ability to play a game, like the ability to use the words of a language, is mastery of a technique. Playing games, like speaking, is a human activity, and the existence of shared games, like a shared language, presupposes common reactions, propensities and abilities. The ‘gap’ between rules and their application, which is bridged by training and familiarity with the practice of playing, is in plain view (which is one reason why the comparison with games sheds light on our linguistic practices, in which this ‘gap’ is shrouded in darkness). The goal of a game, to the extent that it is a winning and losing game, is determined by the rules of the game (which stipulate what counts as winning) and is not extraneous to it — even though one may play for pleasure, fame or money. Language too cannot be said to be deﬁned by any extraneous goal, such as communication (see Exg. §§491–500). The comparison with chess remained fruitful, for the chess analogy makes it easier to resist the temptations to mystify and mythologize in the domain of language. Indeed, it becomes a more useful analogy in the new context, since it preserves, qua analogy, the valuable features that were captured (even though distorted and exaggerated) by the calculus conception of language. But it is now exploited for the characteristics of chess as a game, which illuminate the concept of a language. (i) The outward similarity of words is comparable to that of chess pieces, and no less misleading (PG 59). But there is less temptation to idealize chess pieces (to think that the chess king, not being just a piece of wood or ivory, is an abstract entity (PI §108)) than there is to Platonize or psychologize wordmeanings (to think that they are abstract entities in a ‘third realm’, or ideas ‘in the mind’). (ii) The question ‘What is a word?’ is analogous to the question ‘What is a chess piece (say, the king)?’ (PG 121; PI §108). (iii) The combinatorial possibilities of words are comparable to the possible conﬁgurations of chess pieces. (iv) Rules that exclude certain combinations of words as senseless (e.g. ‘Nothing can be red and green all over’) are comparable to the chess rule prohibiting two pieces on the same square (PG 125). (v) The use of a word in an utterance is like the use of a chess piece in a move.

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(vi) The meaning of a word is analogous to the powers of a chess piece. (vii) Just as a chess piece has signiﬁcance, fulﬁls a role, only in the context of a move, so too, a word fulﬁls a role in saying something only in the context of a sentence, for, with minor exceptions, a sentence is the minimal move in the language-game (see ‘Contextual dicta and contextual principles’, sect. 1). (viii) A chess move is a move only in a game,8 and a sentence is a sentence only in a language (cf. PG 172). (ix) Understanding a word is not a mental state, event or process, but (with qualiﬁcations) an ability to use it in certain ways for certain purposes, just as knowing how to play chess is knowing how to move the pieces in conformity with the rules of chess in pursuit of the goal of winning. In both cases a technique is mastered. Nevertheless, as with all analogies, there are hidden dangers in the analogy between playing a game and speaking a language — of exaggeration, and of forgetting that we are dealing only with an analogy. It is important to bear in mind the following. (i) Speaking a language is not playing a game. (ii) There are many different games, as there are many different languages. But there is no such thing as translating football into cricket or chess into tiddlywinks, as one can translate English into German or into Chinese. (On the other hand, one cannot translate one language-game into another either.) (iii) In so far as we are to conceive of a language and speech as akin to a motley of language-games and playing them, we must bear in mind that while one game is not interwoven with another (football and poker, say), the various language-games we play are systematically interconnected. They are all parts of the larger whole of our language and speech, and the language-game of giving orders and obeying them (PI §23) is interwoven with the languagegames of reporting an event (e.g. of the giving or obeying of an order) or speculating about an event (e.g. whether an order will be obeyed), and the language-game of asking (PI §23) is systematically connected with the languagegames of thanking (e.g. thanking someone for answering) or cursing (e.g. cursing someone for asking) or describing (e.g. describing someone as asking), and so on. (iv) Many games involve winning and losing, but there is no good analogue of this in the case of speaking a language. Saying something true is not winning; nor, in the relevant sense, is telling a successful lie. (v) Moving a chess piece, scoring a goal or hitting a six do not describe, truly or falsely, how things are. Nor do moves in a game constitute the asking of questions as to how things are. Nor is a move in a game, as such, an order or a request to bring it about that a certain state of affairs obtain. 8

Of course, one may make a chess move in the context of solving a chess puzzle. But that is not an exception to the point Wittgenstein has in mind.

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(vi) By and large, all games and playing of games beyond the most primitive presuppose language, but language and its use do not presuppose the existence of games. One can imagine beings who speak a developed language but do not play games, but not beings who play developed games but do not speak a language. None of this detracts from the power or illumination of Wittgenstein’s analogy. It merely indicates the need for care.

2. An intermediate phase: comparisons with invented calculi In the late 1920s Wittgenstein apparently held that logical analysis will reveal that the gross material object propositions of natural language are reducible, in the depth grammar of the calculus of language, to propositions about immediate experience (e.g. visual impressions). He wrote of this in 1936: Formerly, I myself spoke of a ‘complete analysis’, and I used to believe that philosophy had to give a deﬁnitive dissection of propositions so as to set out clearly all their connections and remove all possibilities of misunderstanding. I spoke as if there was a calculus in which such a dissection would be possible. I vaguely had in mind something like the deﬁnition Russell had given for the deﬁnite article, and I used to think that in a similar way one would be able to use visual impressions etc. to deﬁne the concept say of a sphere, and thus exhibit once and for all the connections between concepts and lay bare the source of all misunderstandings, etc. At the root of all this was a false and idealized picture of the use of language. (PG 211)

Similarly, in 1929 he held that what was essential in personal experience would be more perspicuously represented by a notation without the ﬁrst-person pronoun. He wrote: One of the most misleading representational techniques in our language is the use of the word ‘I’, particularly when it is used in representing immediate experience, as in ‘I see a red patch’. It would be instructive to replace this way of speaking by another in which immediate experience would be represented without using the personal pronoun; for then we’d be able to see that the previous representation wasn’t essential to the facts. Not that the representation would be in any sense more correct than the old one, but it would serve to show clearly what was logically essential in the representation. (PR 88)

Consequently, he sketched such a notation, with an oriental despot as its ‘Centre’ (WWK 49). When the despot is in pain, he says ‘There is pain’; and when anyone else is in pain, it is said that he is behaving as the Centre behaves when there is pain. In his 1929 paper ‘Some Remarks on Logical Form’, he asserted that ordinary language disguises logical structure, and needs to be replaced, for philosophical

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purposes, by a symbolism that gives a clear picture of the forms of phenomena represented. ‘We can only arrive at a correct analysis by, what might be called, the logical investigation of the phenomena themselves, i.e. in a certain sense a posteriori’ (RLF 163). And the upshot of his investigation was that atomic propositions predicating colour must, on analysis, contain rational and irrational numbers (to deal with gradations of a colour). This, he wrote, ‘is not merely a feature of a special symbolism, but an essential and, consequently, unavoidable feature of the representation’ (RLF 166), for only thus will the representation have the right logical multiplicity that will reﬂect the objective, languageindependent form of colours. Evidently, at this stage in the development of his thought, Wittgenstein held not only that the surface grammar of natural language is deceptive, but further, that it conceals the logico-metaphysical forms of the facts it represents. Accordingly, an alternative notation can be devised which will perspicuously be faithful to the logical forms of the world. This phase did not last long. As the philosophy of the Tractatus crumbled, Wittgenstein abandoned the whole picture of isomorphism between language and the reality it depicts. He came to reject the very idea of a calculus underlying the ﬂuid forms of natural language, a calculus that faithfully and perspicuously reﬂects the forms of the facts it can be used to depict. However, the now rejected calculus conception left an afterglow, which survived for some time. Three features bear on our current concerns. First, throughout the early and mid-Thirties, Wittgenstein recurrently emphasized that although language is not determined by a system of strict or exact rules, he, in his investigations, will constantly compare it to such a calculus (PG 63, 68, 77; BB 25). We do not use language according to strict rules that determine sharp boundary lines for concepts. If we are asked for exact deﬁnitions of our terms, we cannot give any, not because we are ignorant of the deﬁnitions, but rather because, for the most part, they are not used according to such strict rules. To suppose that there must always be a strict deﬁnition is like supposing that whenever children play with a ball they must be playing a game according to strict rules. When philosophers conceive of language on the model of a calculus, what they have in mind is to be found in the sciences and in mathematics, but natural language only rarely conforms to this model. Why, then, is there any point in comparing the ﬂuidity of natural language with a calculus? Because certain puzzles and philosophical troubles that Wittgenstein aims to address arise from conceiving of a language as a calculus, and from making up too simple a system of rules (BB 25; AWL 48). One might have expected him to illustrate the latter point with examples derived from the Tractatus or from its style of thought. But in the Blue Book Wittgenstein’s two illustrative examples are Augustine’s puzzle about time and Socrates’ quest for a deﬁnition of knowledge. This is surprising, since Augustine’s puzzle stems primarily from conceiving of the measurement of time by analogy with the measurement of space, and Socrates’ puzzles about

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knowledge stem from a misguided quest for a strict deﬁnition, where there is none. It would be misleading to say that these puzzles stem from a conception of natural language as a calculus.9 Given Wittgenstein’s declaration that he will ‘constantly compare language with a calculus proceeding according to exact rules’ (BB 25), one might expect that we should ﬁnd such comparisons throughout the Blue and Brown Books. In fact, we do not — what we ﬁnd is the emergence, in the Brown Book, of the language-game method (of which more in a moment). To ﬁnd Wittgenstein ‘constantly comparing’ language (or parts of language) with a calculus, we must turn to The Principles of Linguistic Philosophy (the abandoned fruit of his dictations to Waismann (VoW)). For it is here, very brieﬂy, that we ﬁnd him employing the method that he had announced. In chapter IV, entitled ‘Grammatical models’, Waismann writes: We do not want to dogmatize, but we leave language as it is and set beside it a grammatical picture, the features of which are perfectly under our control and in which, therefore, we can set up exact rules. We construct, as it were an ideal case, but without pretending that it agrees with anything. We construct it only in order to gain a compendious scheme with which we can compare language. Thus we become aware of an aspect which, since we do not claim it to be true, cannot be false either. . . . . . . We draw up lists of rules parts of which run parallel to those of ordinary language, and which serve the purpose of eliminating the difﬁculties which can be eliminated through setting up such rules. We need not therefore make any assertion, say, for instance, that this or that is the real meaning of the statement. Indeed such a way of speaking is dangerous, it tempts one to try to arrange the reality of language according to a particular pattern, if not to alter it to ﬁt the pattern. We need not do anything of this sort. We simply place the pattern beside language and let it throw as much light upon its nature as it can. (PLP 72, 77)

To illustrate this method, Waismann (following Wittgenstein) applies it to the question of whether propositions about physical objects can be analysed in terms of sense-data (cf. PG 211, quoted above).10 Suppose we take as an example ‘There is a cube on the table’. Suppose we ﬁnd an equation which enables us to construct the occlusion-shape of the cube from any point in surrounding space. So from speciﬁcation of the object and the position of an observer, we can construct the occlusion-shape by means of the equation, and from the law 9 But one might well say that the Platonic quest for deﬁnitions is rooted in the misleading model of the calculus of geometry. 10 It is evident that Waismann’s remarks are mediately dependent on Wittgenstein’s 1929 discussions of what he called ‘hypotheses’. This can be seen by comparing PLP, ch. IV with PR 282–8. Waismann’s source was Wittgenstein’s dictation (VoW 345ff.). The conception of hypotheses as laws for constructing ‘genuine propositions’ and of statements of immediate experience as the ‘genuine propositions’ was one which Wittgenstein was rapidly to abandon. It continued to inﬂuence Waismann, however, and it informs his papers ‘Language Strata’ and ‘Veriﬁability’, repr. in F. Waismann, How I See Philosophy, ed. R. Harré (Macmillan, London, 1968).

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determining the changing occlusion-shape, we can pass to the ordinary description of the body. If it is asserted that there is a cube on the table, we can, with a set of drawings of the occlusion-shape from a number of points, check what is seen against the drawings (as it were, verifying the descriptions of the occlusion-shapes (cf. PR 284)). Now, to be sure, we do not verify that there is a cube on the table in this way in reality. But what we have described in this imaginary procedure ‘is a game in its fully developed form’ (PLP 73). It helps us see more clearly what actually happens, or ‘at any rate it bears a certain resemblance to the actual use of the sentence in question. We intentionally construct a hypothesis in which there are exact predictions and exact checks on these predictions. We then consider the actual use of “A cube is lying here” in the light of the similarity it bears to the case we have constructed’ (PLP 73f.). Waismann then gives a further illustrative example: Do material object statements admit of conclusive veriﬁcation? Here too various calculi can be imagined, and Waismann concludes: In the grammatical models just constructed we were free to determine a ﬁnal criterion of veriﬁcation or to adopt a hypothesis in such a way that no criterion is permitted. If asked what is meant by the assertion that a ball is lying on the table, when used in daily life, we would have difﬁculty in replying . . . a great number of distinct grammatical models can be set beside the assertion about the ball which to a greater or lesser degree match this assertion. And here the matter must rest. (PLP 75)

This seems to be the extent of Wittgenstein’s temporary commitment to the idea that ordinary language is everywhere ﬂuid, and that philosophical clariﬁcation can come from juxtaposing invented calculi with the problematic fragment of natural language in order to highlight similarities and differences. This method rapidly gave way to the method of language-games.11

3. The emergence of the language-game method The idea of a language-game ﬁrst occurs in the surviving manuscripts in March 1932 (MS 113 (Vol. IX), 45r; cf. MS 115 (Vol. XI), 80)), although it may well have been introduced earlier in now lost notebooks. Wittgenstein 11

There is another idea with which Wittgenstein seems to have toyed, which emerged from the abandoned method of juxtaposing expressions of ordinary language with expressions in a sharply determined calculus. In the ‘Yellow Book’ (notes taken from dictation by Alice Ambrose in 1933–4, some of which are published in AWL 41–73), he observes ‘in discussing understanding, meaning, etc. our greatest difﬁculty is with the entirely ﬂuid use of words. I shall not proceed by enumerating different meanings of the words “understanding”, “meaning”, etc., but instead shall draw ten or twelve pictures that are similar in some ways to the actual use of these words’ (AWL 48; see also BB 27: ‘There is no one exact usage of the word “knowledge”; but we can make up several such usages, which will more or less agree with the way the word is actually used’). However, nothing more is heard about this Galtonian method after the mid-1930s.

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introduced a game of saying ‘Light’ in response to an electric light’s being turned on and ‘Dark’ in response to its being turned off. This is then used to investigate the difference between a word and a sentence, a description and an expression of a wish. Wittgenstein emphasized that the point of describing language-games is not progressively to construct the real processes of talking or thinking, but only to provide an object of comparison for the particular case. In the picture of the ordinary use of an expression, the different colours, as it were, ﬂow into one another without sharp boundaries. We can juxtapose this picture with another that resembles it in various ways but which is built up of colours with clear boundaries between them. Then we can let the latter shed light on the former (cf. PG 76). Language-games are introduced in the Blue Book thus: I shall in future again and again draw your attention to what I shall call languagegames. These are ways of using signs simpler than those in which we use the signs of our highly complicated everyday language. Language-games are the forms of language with which a child begins to make use of words. The study of language-games is the study of primitive forms of language or primitive languages. If we want to study the problems of truth and falsehood, of the agreement and disagreement of propositions with reality, of the nature of assertion, assumption and question, we shall with great advantage look at primitive forms of language in which these forms of thinking appear without the confusing background of highly complicated processes of thought. When we look at such simple forms of language, the mental mist which seems to enshroud our ordinary use of language disappears. We see activities, reactions, which are clearcut and transparent. On the other hand we recognize in these simple processes forms of language not separated by a break from our more complicated ones. We see that we can build up the complicated forms from the primitive ones by gradually adding new forms. (BB 17)

This observation is striking, since the ﬁnal remark appears prima facie to conﬂict with the disclaimer of 1932. But having thus introduced and explained the point of the novel notion, Wittgenstein, surprisingly, does not employ it in the Blue Book at all. It is in the Brown Book that the language-game method comes to maturity, and arguably is used to excess. Here Wittgenstein notes that language-games are more or less akin to what in ordinary language we call games. Children are taught their native language by means of such games, and here they even have the entertaining character of games. We are not, however, regarding the language games which we describe as incomplete parts of a language, but as languages complete in themselves,12 as complete systems of human communication. To keep this point of view in mind, it very often is useful to imagine such a simple language to be the entire system of communication of a tribe in a primitive state of society. (BB 81) 12

EPB 121 modiﬁes this: ‘not as fragments of the whole of “language as such”, but as simple, primitive, languages complete in themselves’.

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In the Investigations, Wittgenstein introduces the concept of a language-game in relation to the builders’ language in §2. He then observes: ‘We can also think of the whole process of using words in (2) as one of those games by means of which children learn their native language. I will call these games “languagegames” and will sometimes speak of a primitive language as a language-game’. (PI §7). We must accordingly distinguish three different aspects of Wittgenstein’s language-game method. First, he often invokes the primitive language-games by means of which the child begins to master various fragments of our language. Wittgenstein uses these to illuminate the mature language-game of which they are a primitive core or centre of variation. So, it is illuminating to be reminded of the fact that the child learns the language-game with ‘pain’ as a partial substitute for natural cries of pain (PI §244).13 It is a feature of our biological nature that we scream or cry with pain. The young child rapidly learns to replace the natural cry by an ‘Ow’ (or, in some cultures, an ‘Aya’, or a ‘Weh-weh’, etc.); subsequently he learns the primitive use of ‘Hurts’. Later still, ‘I have a pain’ supplements ‘Hurts’ and ‘It hurts’. Of course, this use of ‘I have a pain’ is only one, and using the same sentence in cool reports of pains, or using the past tense, or using the sentence as the antecedent of a conditional, etc. are all more or less removed from it. Nevertheless, it provides an important and illuminating core. Similarly, it sheds light on the concept of intention to be reminded that one way we might teach a child to use rudimentary expressions of intention is by teaching it the primitive language-game of saying ‘I’m going to . . .’, in which it is a crucial part of the game that when one says ‘I’m going to . . .’, then one goes on to. . . . This is relatively far removed from ‘I intend to see Naples before I die’, but it is an important ‘centre of variation’ in the rich and variegated mature language-game with expressions of intention. Again, it is salutary to be reminded that the child is not taught the use of ‘dream’ and ‘to dream’ by being shown a dream. Rather, we teach a child who wakes up crying that he is afraid of the tiger chasing him to say, ‘I dreamt that a tiger was chasing me’ instead of ‘A tiger was chasing me’, and later to say ‘I had a nightmare’. This is far removed from an adult analysing his or another’s dreams, but it is the core on which those uses of ‘dream’ and its cognates rest. Is this question-begging armchair learning-theory? Not so. It is drawing attention to what lies before our noses, to ‘aspects of things that are . . . hidden 13

Wittgenstein introduces this observation on how a human being learns the names of sensations with the preface ‘Here is one possibility’. It is not at all clear whether this is meant as a serious qualiﬁer or not. In view of the frequency with which he connects the use of ‘I have a pain’ with natural pain-behaviour, and of the fact that in PI §244 he goes on to assert without qualiﬁcation that what he is saying is that ‘the verbal expression of pain replaces crying and does not describe it’, it is plausible to think that it is not so much a qualiﬁer as a pointer to the fact that there are other ways of teaching someone what the English word ‘pain’ means, one of which is given in PI §288.

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because of their simplicity and familiarity’ (PI §129). But nothing turns on the empirical veriﬁcation of these humdrum observations, and if anyone wishes to contest them on empirical grounds, one may simply say that these are ways in which the expression might be taught. For that alone sufﬁces to shake the grip of the misconceived alternatives that bedevil philosophical reﬂection, e.g. in the empiricist tradition. Secondly, Wittgenstein commonly invents language-games that resemble those a child learns, but are to be considered ‘complete’. He notes in the Brown Book that the primitive language-games the child learns are fragments of larger wholes, relative to which they are incomplete. But frequently, for the morphological purposes (see ‘Surveyability and surveyable representations’, sect. 3) for which Wittgenstein introduces them, the primitive games he discusses should not be seen thus. Viewed as complete in themselves, they are to be placed alongside our more complex and ramifying games, which are played in more complex contexts. The primitive but complete game is intended to shed light, by way of similarities and differences, on our practices. Hence he observes that ‘It disperses the fog to study the phenomena of language in primitive kinds of application in which one can command a clear view (übersehen) of the aim and functioning of words’ (PI §5). These primitive language-games, which typically resemble fragments of our own language-games, illuminate our practices. For they reveal what complex concepts have a place in the description of our language, but not in the primitive context — and they show why this is so. They make evident some of the deep contextual presuppositions of our language-games, which are covered up by their complexities and ramiﬁcations. They often isolate a feature analogous to some feature of our language, but which, surrounded by the ordinary circumstances of its use, is not easily brought into view. Thirdly, Wittgenstein sometimes invents imaginary language-games for purposes quite different from creating an illuminating, more or less homologous object of comparison for a fragment of our language. Rather, his purpose is to clarify the defects of particular philosophical misconceptions. So, the ﬁrst language-game in the Investigations is introduced to provide a model language for which Augustine’s account of how he had learnt Latin as a child is apt — thereby highlighting how inappropriate it actually is, and revealing how deeply misconceived is the conception of language and linguistic meaning implicit in Augustine’s ruminations. The language-game with coloured squares in Investigations §48 does similar service for Plato’s conception of primary elements and the Tractatus account of simple names signifying simple objects. It provides a model, and makes clear what was awry with the conception of sempiternal simples and simple names. Somewhat differently (but as a natural extension of the second kind of case), Wittgenstein sometimes asks us to imagine primitive language-games played in fundamentally different circumstances from those in which we play ours. We are called upon to envisage a colour vocabulary that would be useful in

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a world in which almost all coloured objects have colours at the cold end of the spectrum, and in which reds, oranges and yellows occur only rarely and typically in combination and perhaps associated with a particular natural phenomenon. Or we might try to envisage a world in which people’s natural reactions are different in certain striking ways from ours, or in which natural reactions (of laughter, or of tears, etc.) are not shared as they are with us, or in which people’s powers of surveying things was greater or lesser than with us. Reﬂection on the language-games that might be played in such circumstances by such people helps to shake the grip of the thought that our concepts are the only possible ones, or that they are uniquely correct. And it clariﬁes the fact that our conceptual scheme is conditioned in various ways by the regularities of the world and the regularities of natural human reactive and discriminative behaviour.

4. Invented language-games Wittgenstein’s invented language-games display a disjunctive range of features which are given varying prominence for the philosophical purposes for which they are invoked. (i) Words, and sentences formed from them according to combinatorial rules; the vocabulary is given, and its use in speech-acts (moves in the language-game) speciﬁed. (ii) Instruments (PI §§291, 569; BB 84): in the Brown Book Wittgenstein calls ‘instruments’ (a) gestures, as used in teaching the use of ‘there’; (b) patterns, whether samples, words or ﬁgure drawings; and (c) pictures in a table which correlates words and pictures. This accords with his favoured tool analogy for words. It extends the concepts of language and grammar to include elements hitherto regarded by linguists and philosophers as extraneous. (iii) Context (Zusammenhang): it is important to distinguish the generality of the notion of context that is being used and the purpose for which it is brought into view. Like any other game, a language-game is ‘played’ in a setting. Wittgenstein’s stress on the context of the game appears to be motivated by the wish to bring to the fore elements of linguistic activities which, while not obviously involved in the explanation of the meaning of constituent expressions (hence unlike instruments), are nevertheless pertinent to their meaning. At its most general the notion of context encompasses the presuppositions of meaning. If the context were signiﬁcantly different, the game would not be played, for it would be pointless. Every game has its normality conditions, the obtaining of which are presupposed by the game (Z §350). These may be very general features of the natural world, e.g. the rigidity and non-elasticity of material objects and of measuring rods, and equally general features of humanity, e.g. agreement in responses (to injury, colour, pointing, etc.). They may, however, involve more speciﬁc features, peculiar to a very particular

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language-game of, say, a small linguistic group, e.g. interests and values (Z §380), special activities such as battles (PI §19), building (PI §2), contests (BB 110), as well as the availability of particular types of object (e.g. buildingstones, colour samples, etc.). We must distinguish context understood (a) as a presupposition of the existence of a game; (b) as a presupposition for the actual playing of that game on a given occasion; (c) as the colouring, as it were, of the game. (iv) The use, purpose, role and function of instruments, words, sentences (and occasionally even language-games themselves): this is a family of concepts which play a central role in Wittgenstein’s philosophy. It was, he said, the ‘main mistake of philosophers of the present generation (including Moore)’ that they focused upon the forms of expressions rather than upon the use made of these forms (LA 2). (v) Learning: we learn language-games and the foundation of this learning is training (Z §§387, 419). In many of his invented language-games Wittgenstein sketches the different kinds of training necessary for a participant to be able to play (e.g. memorizing words, memorizing the sequence of natural numbers, learning the practice of comparison of samples, or the method of projection of a pattern, etc.). Illuminating the differences in kinds of training in the use of different words clariﬁes the logical diversity of kinds of words (numerals, colour-words, names of material objects, etc.). (vi) Teaching: although there is no sharp dividing line between training and teaching, the context and methods of teaching illuminate the presuppositions of explanation, the terminus of explanation, the prerequisites of doubt and question, and the character of grammatical justiﬁcation. (vii) The practise of playing the game: focusing upon the complex practise of playing the game highlights the nature of rule-following and the way in which the ‘gap’ between rules and their application is bridged. This illuminates the internal relation between a rule and what counts, in the practise of playing the game, as acting in accordance with it. (viii) The activities of the game: it is in the activities constitutive of a language-game that the point and purpose of linguistic expressions are evident. Concentration upon the activity which is the playing of a language-game highlights the diversity of linguistic symbols, emphasizes their normal contexts of use, their normal (diverse) purposes, and the normal justiﬁcations for their use. (ix) Completeness: Wittgenstein commonly emphasizes that his invented games are not fragments of a language, but should be considered as complete (P1 §§2, 18; BB 81). This has been discussed above. A caveat: although Wittgenstein continued to use the concept of a languagegame until the end of his life, invented language-games dominated his writing only in the unsuccessful endeavour of the Brown Book. One should bear in mind that in the Investigations (Part 1), only half a dozen or so invented language-games are described.

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5. Natural language-games Wittgenstein also uses the term ‘language-game’ to designate fragments of our actual linguistic practices. He speaks of the language-game with words, e.g. with ‘game’ (PI §71), ‘proposition’, ‘language’, ‘thought’, ‘world’ (PI §96), ‘pain’ (PI §300), ‘read’ (PI §156); also of language-games surrounding characteristic linguistic acts or activities, e.g. lying (PI §249), telling (PI §363), giving orders and obeying them, describing the appearance of an object, or giving its measurement, reporting an event, etc. (PI §23), telling a dream (PI p. 184/157), confessing a motive (PI p. 224/191); and also of more complex activities into which language is woven, but which are not merely speech-acts or activities, e.g. constructing an object from a description, forming and testing hypotheses, presenting results of experiments in tables and diagrams (PI §23), making inductive predictions (PI §630). Occasionally, the term is used even more generously, e.g. the language-games with physical objects and with sense-impressions (PI p. 180/154). The various elements previously isolated with respect to imaginary games apply (with the exception, usually, of completeness) to actual language-games. To the extent that isolation of a natural language-game is possible, it is a matter of highlighting, bringing to the fore, features of linguistic activities so ﬁrmly embedded in our daily practices that we no longer notice them. Thrust forward in this way, we can more readily scrutinize the familiar, see its dependence upon the texture from which we have removed it, compare it with imaginary games deliberately different in signiﬁcant ways. If the similarities between the artiﬁcial language-games which Wittgenstein invented and such a fragment of language are sufﬁciently striking and extensive, it is natural to extend the term ‘language-game’ by applying it also to the fragment itself. It is noteworthy that it is very difﬁcult to ﬁnd any principles of classiﬁcation or individuation for language-games. Wittgenstein characterizes a remarkable motley of activities as different language-games, ranging from items as relatively specialized as cursing or presenting the results of an experiment in tables and diagrams to things as general as giving orders or describing the appearance of an object. Clearly he operates at different levels, corresponding to the problems he is dealing with; but it is unclear how to decide whether or not a given speech activity does or does not count as a language-game, and what counts as the same language-game. Nevertheless, that is no barrier to understanding Wittgenstein’s observations and their purpose. Above all, it is evident that the main point of his stressing the irreducible multiplicity of language-games was to contrast this ‘with what logicians have said about the structure of language. (Including the author of the Tractatus Logico-Philosophicus.)’ (PI §23). For they are prone to reduce everything to descriptions and ‘descriptive contents’ (see ‘Descriptions and the uses of sentences’), as the author of the Tractatus argued

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that all propositions with a sense are pictures (hence descriptions) of possible states of affairs. A primary factor that made the idea of a language-game appealing is its stark contrast with the calculus model that dominated the Tractatus. It provided a powerful analogy which offered a normative (i.e. rule-governed) activity to compare with language and its use, but without the falsiﬁcation that is involved in the idea of a calculus governed by rigid and closed rules. Moreover, the game analogy encourages us to abandon a preoccupation with the geometry of calculi and to focus instead upon the activities into which our symbolism of language is woven. It can therefore be used, as Wittgenstein used it, to emphasize the logical diversity and multiplicity of our speech activities. It highlights the ways in which the variety of speech-acts which we perform by the use of sentences are part of the tapestry of our lives, conditioned in many different ways by the world around us and by our perceptual abilities, our powers of recall and of surveying data, our natural interests and shared responses. For the language-games we play are moulded by the nature of the world we live in and by our nature, and they are partly constitutive of our forms of life (PI §23).

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

IV Descriptions and the uses of sentences 1. Flying in the face of the facts Having explored the Augustinian misconceptions concerning words and naming, Wittgenstein turns, in §§18–27(a), to an examination of correlative misconceptions with respect to sentences. He touches brieﬂy on various topics: on the variety of sentential forms and on the question of whether any one of them, e.g. the declarative form, enjoys relative primacy; on one-word sentences and elliptical sentences; on statements, commands and questions, and the relationships between them; on Frege’s notion that every assertion contains an ‘assumption’ (Annahme); on the multiplicity of kinds of language-games; and on the analysis of discourse-functions and their relation to syntactical forms of sentences. This essay will examine only two strands in this complex web: his criticisms of the idea that all sentences are or contain descriptions, and his diagnosis of the roots of this illusion. It was argued above that a natural extension of Augustine’s picture of the essence of human language is the idea that the fundamental role of sentences is to describe (‘The Augustinian conception of language’, sect. 2(e)). For if the role of words is to name entities in reality, and if sentences are grammatical combinations of words, it is natural enough to suppose that a given grammatical combination of names represents a corresponding array in reality of the entities they name (that they are words for, that they stand for), and so describes how things are. To be sure, the mere assertion that all sentences are descriptions is obviously incorrect. The most cursory reﬂection, stimulated if need be by the list of language-games in §23, shows it to be false. Indeed, it seems that a language might contain no descriptions at all; e.g. it might consist wholly of orders (§18) or questions and yes/no answers (§19). Nevertheless, the conception that all sentences are really descriptions will not be eradicated by confronting it with a truism. For philosophers have not been oblivious to the obvious. Rather, they have argued themselves into the conception of sentences as being essentially descriptions in the face of the obvious. They have insisted that despite appearances, sentences must be descriptions, otherwise they would not be able to do various things which they seem to do. The drive to ﬁnd descriptions hidden beneath the surface grammar of sentences that in appearance are patently not descriptions (e.g. imperative sentences used to issue orders (to request, entreat, beg), optative sentences used

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to express wishes or longings, exclamatory sentences or interrogative sentences used to ask questions) is motivated by the demands of a particular conception or conceptions of how sentences function. It is clear enough how Wittgenstein himself had been driven by theoretical requirements. In the Tractatus he had argued that all propositions with a sense depict (or describe) states of affairs that may or may not obtain. The unasserted proposition shows its sense, and its assertion says that its sense is actualized (obtains). It appears (NB 96) that Wittgenstein held that the order to bring it about that p and the question of whether it is the case that p depict (or describe) the same state of affairs as the assertion that p, but do not say that the sense obtains. Rather, they (respectively) order it to be brought about (to be made real, as it were) and query whether it obtains. In all such cases, the description of a possibility (a state of affairs) is presented; what differentiates the cases is whether what is thus described is said to obtain, or whether it is asked whether it obtains, or whether the addressee is ordered to make it obtain. So the primacy of description implicit in the Tractatus was driven above all by the requirements of the picture theory of the proposition, which was designed to explain the intentionality of the proposition (Satz) and the possibility of its being false but meaningful (see ‘Turning the examination around: the recantation of a metaphysician’, sects 2–3; ‘Truth and the general propositional form’, sect. 1; and Volume 4, Part I, ‘Intentionality’, sects 1–2). Other philosophers have been driven by other theoretical demands and commitments. Frege’s hypostatization of senses or ‘thoughts’ was driven in part by his anti-psychologism and the illusion that this is the only way to guarantee the objectivity of truth and to ensure the possibility of different people entertaining, agreeing or disagreeing about the same thoughts. Having reiﬁed the thought, i.e. the proposition or sense of a sentence (as Frege conceived it — very differently from Wittgenstein), it seemed evident that this abstract entity was common to an assertion, a corresponding supposition, antecedent of a conditional, and content of a sentence-question. No doubt both philosophers, and others too, were impressed by the fact that there are obvious internal relations between sentence-questions and corresponding assertoric answers, and between orders and corresponding descriptions of compliance or noncompliance. The question of whether it is the case that p is the very question that is answered by the assertion that it is the case that p, and so too the order to bring it about that p is the very order compliance with which is described by the assertion that the addressee has brought it about that p. It is very tempting to explain such internal relations by reference to the fact that the assertion and corresponding command and question share a common descriptive content. Otherwise, how would one, for example, know what one was ordered to bring about? We shall return to this matter below. Other factors came to dominate philosophical reﬂection after Wittgenstein’s death. From the 1960s and 1970s the idea of constructing a theory of meaning for a natural language preoccupied analytical philosophers of language in

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Britain and the USA. This enterprise could not even get off the ground unless it is the case (and can be shown to be the case) that non-assertoric sentences contain a component (a ‘sentence-radical’ (PI p. 11/9n.), or a ‘phrastic’ (in R. M. Hare’s jargon1)), that has a sense (a descriptive content) and can be said to bear a truth-value. This descriptive content must be common to non-assertoric sentences and the corresponding assertoric sentence. For pivotal to such programmes for a theory of meaning for a natural language was the concept of a truth-condition.2 The meaning or sense of a sentence, i.e. what is said by its use, was held to be given by specifying its truth-conditions. The meaning of a word was held to consist in its contribution to the determination of the truth-conditions of any sentence in which it occurs. But since words occur in non-assertoric sentences, the latter must, contrary to appearances, contain a truth-value-bearing component. Otherwise the words that occur in them would either have no meaning or a meaning distinct from the meaning they have in assertoric sentences. And that is surely absurd. The distinction between ‘sense’ (conceived as a descriptive content) and ‘force’ (signiﬁed by a ‘mood-operator’) was a sine qua non of the enterprise, and hence a powerful motive for insisting that on analysis, every sentence is or contains a description of a state of affairs. This conception of a theory of meaning will not be discussed here. But it should be obvious that Wittgenstein’s reﬂections have a direct negative bearing on it.

2. Sentences as descriptions of facts: surface-grammatical paraphrase Confronted by the evident fact that sentences have very different uses, not merely to describe how things are but to do many other, different, things, one might, if one has a theoretical axe to grind, admit that they have different uses, but explain the differences in use by reference to the differences in the facts described. This will preserve the thesis that the essence of sentences is to describe. This thought may be fostered by two manoeuvres: ﬁrst, by interpreting various forms of paraphrase that are available in our language to show that what appear to be different uses (e.g. of declarative sentences, on the one 1

R. M. Hare, The Language of Morals (Oxford University Press, Oxford, 1952), ch. 2. Hare’s motivation was a logic of imperatives. Philosophers who advocated the programme of constructing a theory of meaning for a natural language and who adopted one or another variant of this form of analysis were, e.g., D. Davidson and M. A. E. Dummett. 2 It should be noted that the notion of a truth-condition had undergone a sea change since its introduction in the Tractatus (and its earlier brief appearance in Frege’s Basic Laws i §32). For according to the Tractatus, a truth-condition is a condition a proposition has to satisfy in order to be true. So, for example, the truth-condition of a conjunction is that both conjuncts be true. But in the wake of Tarski, it became common to speak of the truth-conditions of an atomic proposition. So a truth-condition was no longer a condition that had to be met by such a proposition (that snow is white is not a condition which the proposition that snow is white could intelligibly be said to satisfy).

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hand, and interrogatives or imperatives, on the other) are nevertheless really descriptions; and secondly, by insisting on the variety of kinds of facts described, which seems to explain why different grammatical forms, despite appearances to the contrary, nevertheless fulﬁl the same descriptive function. So, one might argue that a question sometimes describes the speaker’s state of ignorance, sometimes his desire to be informed of something, for one can paraphrase a question by such sentences as ‘I want to know whether . . .’ or ‘I wonder whether . . .’ (PI §24). By parity of reasoning, one might think that orders, commands and requests are really descriptions of what the speaker wants the addressee to do, for they can be paraphrased by ‘I would like you to . . .’ or ‘I want you to . . .’. So, for example, Russell held that ‘It may be that questions and commands can also be regarded as statements, but if so, they can be expressed in terms which are no longer grammatically questions or commands’ (TK 105f.). The second kind of manoeuvre yields a richer harvest. The expression of a rule, one might claim, does not describe what is the case but rather what ought to be the case (PLP 143). A description of a house in a novel, one might say, describes a ﬁctional, not an actual, fact. Modal propositions concerning what might be the case describe possible facts. Similarly, propositions that assert that something must be so describe necessary features of the world. Mathematical propositions, Platonists aver, describe relations between numbers, i.e. mathematical facts. And logical propositions have been thought to describe the most general facts in the universe (Russell) or the most general relationships of thoughts (Frege). There seems to be no limit to the kinds of facts that we can distinguish, and hence it can seem as if apparent differences in the uses of sentences are superﬁcial, concealing a uniformity of use. For the apparent differences can always be represented as differences in what is described. Wittgenstein criticizes such moves. (i) The point of calling a sentence a description is presumably to characterize it as having a particular use. But even what are ordinarily called ‘descriptions’ are already logically heterogeneous, with profoundly different uses (PI §§24(b), 290f.; see Exg.). Describing the room one is in, the childhood nursery one remembers, one’s room as it will be when one has repainted and rearranged it, one’s dream of a room, the architect’s drawings of a room that is to be constructed, the archaeologist’s reconstructive drawing of a room he has excavated, the novelist’s description of a room in his novel, etc. are very different language-games. Reﬂect on what (if anything) counts, from case to case, as the truth of the description, as improving the description, as evidence for it, as correcting it. We call all this (and much more too) ‘describing’ and ‘description’, and these terms already mask the logical diversity of the activities and the uses of the forms of words in question. (ii) Further extension of ‘description’ beyond its already heterogeneous varieties aggravates the problem. If we characterize statements of rules as descriptions of what must or should be done (of ‘normative facts’), if we characterize

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the propositions of arithmetic as descriptions of relations between numbers and propositions of geometry as descriptions of space (or of Ideal or Platonic Forms), if we characterize expressions of intention, disbelief or anger (e.g. ‘I’m going to go’, ‘I can’t believe it!’, ‘I won’t stand for it!’) as descriptions of mental states, we merely bury logical diversity beneath a façade of formal similarity. Consequently, even if all sentences had the form of information (description), it would not follow that they had a uniform use (RC §336). (iii) It is an illusion to think that the possibility of paraphrasing interrogative or imperative sentences into the form of a description proves that understanding non-descriptive uses of language is not fundamental for understanding language. Consider the paraphrase of ‘Is it the case that p?’ into ‘I would like to know whether it is the case that p’ or ‘I do not know whether it is the case that p’. Each of these ‘descriptions’ contains an indirect question. How is it to be understood (cf. TS 211, 598)? Would it not have to be explained by reference to the corresponding direct question? (iv) Treating every sentence as a description distorts the connection between understanding an utterance and reacting to it. If whatever a person communicates in saying something is a description of some fact, then understanding what he says seems to be simply a matter of taking in that information. What one does in response to it is, it seems, something altogether independent (PI §363). Similarly, comforting someone who says ‘I am in pain’ is alleged to be appropriate only because he has conveyed to one the information that he is hurt and because one knows that certain sorts of treatment alleviate pain. This conception distorts the fact that certain behavioural responses to an utterance are criteria for understanding (or misunderstanding) it, and overlooks the fact that some responses to utterances are ‘primitive’ (Z §§537ff.). (v) If every possible sentence in any conceivable language were a description, i.e. if there were no such thing as a sentence which did not function as a description, the term ‘description’ would not have its customary meaning, since it would be extended to cover what are ordinarily not counted as descriptions (e.g. rule-formulations, questions, commands, exclamations, curses). Furthermore, what looked initially like an insight into the nature of sentences and their meanings, is, on further reﬂection, no more than a recommendation to adopt a certain form of representation. We are in effect being advised to adopt a particular array of grammatical forms in which to present the diverse sentences and kinds of sentences of our, and indeed of any, language. But once this is clear, it is also evident that the thesis that every sentence is a description is vacuous. To call all sentences descriptions involves assimilating sentences to a single paradigm in spite of their manifest functional diversity. The conclusion to be drawn from these criticisms is parallel to Wittgenstein’s verdict on the thesis that all words are names. Just as we can explain most words by means of a sentence of the form ‘ “X” signiﬁes . . .’, so we can explain many sentences

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by means of a sentence of the form ‘ “p” describes the fact that . . .’. Yet assimilating the descriptions of the uses of sentences in this way cannot make the uses themselves any more like one another; for, as we have seen, they are absolutely unalike (cf. PI §10). So, too, when we say ‘Every sentence in language describes something’, we have so far said nothing whatever (cf. PI §13), but only committed ourselves to a form of representation.

3. Sentences as descriptions: depth-grammatical analysis and descriptive contents The previous considerations might wean someone from the idea that every sentence is, as it stands, a description of some fact. But this may merely lead one to a more subtle defence of the idea that, despite appearances, every sentence is essentially a description. This becomes clear only when sentences are suitably transformed by analysis. Analysis might extract from every sentence, whatever its use, something which functions as a description. What analysis allegedly exposes is that sentences with different uses may all have an identical descriptive content. Frege, e.g., claimed that a single ‘content of judgement’ was shared by the assertion that p, the question whether p is the case, the assumption that p, and the antecedent in the assertion that if p then q (see Exg. §22). The young Wittgenstein generalized this thesis to commands: ‘Judgement, question and command are all on the same level. What interests logic in them is only the unasserted proposition’ (NB 96). Russell held that the complex gerund of the form ‘Xs being Fs’ signals the proposition that is common to corresponding assertions, questions, commands and expressions of volition. The differences between these, he held, is merely a matter of the different attitudes towards the same proposition that are signalled by the grammatical forms of the sentences (TK 107).3 Against such analyses, the mature Wittgenstein objects (i) to the conception of a ‘sentence-radical’ with a descriptive content common to interrogative and imperative transforms of a declarative sentence, and (ii) to the idea that what differentiates an assertion and a corresponding question or order is the speaker’s attitude towards that common content. (i) The idea that a declarative sentence used to make an assertion contains (on analysis) a constituent (a sentence-radical) with a descriptive content shared with corresponding interrogative and imperative sentences is wrong. This misconception stems from misinterpreting the possibility of paraphrasing sentences used to make assertions into that-clauses preceded by an operator ‘It is asserted . . .’ or ‘It is the case . . .’, and the correlative possibilities of paraphrasing interrogative sentences into that-clauses preﬁxed by ‘Is it the case . . .’, and imperative sentences into that-clauses preﬁxed by ‘Make it the case . . .’ 3

It was this style of analysis that was cultivated by theorists of meaning in the 1970s.

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(PI §22(a)).4 Independently of this possibility of paraphrase, there is no such thing as ‘a sentence-radical with the descriptive content of a sentence’ to play the requisite role of expressing the sense of a declarative sentence while being in principle unﬁt for expressing its ‘force’, i.e. of being used, as a declarative sentence is used, to make an assertion. Like Frege’s ‘assumption’, the descriptive content of a sentence must be a dependent entity. So it must be represented by an expression that cannot be used in isolation to make assertions, ask questions, issue orders, etc. (i.e. by a sentence-radical). Hence it cannot be represented by a sentence. The obvious candidate for so expressing the descriptive content of a sentence is a that-clause. Two considerations support this choice. First, that-clauses lend themselves to the above paraphrases. Secondly, a that-clause is often used in indirect speech to report what someone has asserted, ordered, etc., and hence it seems to express what was asserted or ordered (i.e. a descriptive content which may be common to assertions, orders, questions, etc.). But the sense of a that-clause cannot be identiﬁed with the sense of any sentence.5 For unlike a sentence, a that-clause cannot be used to make a move in a language-game. So, again, what expresses the descriptive content of a sentence (a thought, assumption or content of judgement) cannot be a sentence, but if it is not a sentence, its sense cannot be the sense of a sentence. But the whole point of the manoeuvre was to isolate a descriptive content that is the sense common to a sentence used to assert that p, the sentential antecedent of a conditional that if p then q, the sentence used to ask whether p, and the sentence used to order to bring it about that p.6 It should be noted that this objection does not prohibit stipulative introduction of an assertion-sign to ﬂag sentences, whether atomic or compound, that are used assertively. The assertion-sign could be given various roles, e.g. as a punctuation mark to indicate the beginning of a sentence, thus distinguishing the linguistic unit being used to make a move in the language-game from subordinate elements within that unit; or, to distinguish an assertion from a ﬁction (PI §22(c)–(d)). Nor does the objection deny the possibility of paraphrasing declarative and interrogative sentences into that-clauses plus an operator. The objection is to the contention that every sentence used to make an assertion ‘contains’ a descriptive content that is the sense of the sentence and is common to this assertion, to the order given by uttering a corresponding imperative, to the question asked by uttering a parallel interrogative sentence, etc. In addition, the objection warns us against misinterpreting the signiﬁcance of the possibility of paraphrase. (a) That we can paraphrase sentences into that-clauses plus the appropriate operator no more shows that every assertion, question or command, etc. 4

Russell’s gerundive paraphrase does not differ in principle. Indeed, Frege acknowledged this point by identifying the reference of a that-clause with the sense of the sentence contained in it. 6 For more detailed discussion of Wittgenstein’s objections to Frege’s analysis, see Exg. §§21f. and Exg. p. 11/9n. 5

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contains a description in the form of a that-clause than the possibility of paraphrasing every statement into the form of a question followed by a ‘Yes’ (e.g. ‘Is it raining? Yes!’ = ‘It is raining’) shows that every statement contains a question (PI §22(b)). (b) It would be mistaken to think that the paraphrase provides a uniquely perspicuous expression of an assertion, request, question, etc., a form of words that necessarily carries its use upon its face. ‘I would like to know whether p is true’, ‘You ought to go home’, or ‘The chess queen stands upon its own colour at the beginning of the game’ are all declarative sentences, but paraphrasing them into ‘It is the case that I would like to know whether p is true’, ‘It is the case that you ought to go home’, and ‘It is the case that the chess queen stands upon its own colour . . .’ does not render their meaning more perspicuous. It merely serves to obscure their manifestly different uses by a canonical form. (c) We should not follow Frege and Russell in thinking that projecting sentences used to assert something on to the articulated form of assertion-sign and sentence-radical is also an anatomization of the act of asserting into two components, e.g. entertaining and judging (PI §22(c)). It would, after all, be absurd to claim that in saying that if p then q, or indeed that if it had been the case that p it would have been the case that q, one has entertained the supposition that p, let alone that one has supposed that p. It would be misconceived to suggest that in ordering someone to bring it about that p, one was also ‘supposing’ or ‘entertaining the thought’ that p. (d) Since an asserted sentence, a question, etc. need contain no that-clause, the thesis that every assertion, question, etc. has a descriptive content is most naturally construed as the claim that the act of making an assertion, asking a question, etc. consists in part in the relation of a speaker to an abstract entity. The idea informing such a picture is that there is a distinct act (‘entertaining a thought’) that is an ingredient in every act of using a sentence to assert something, to ask a question, to formulate a rule, etc.; or, that there is a distinct act (‘understanding the propositional content’) that is an ingredient in the full understanding of a sentence used to make an assertion, etc. The thesis of common content thus reinforces the misguided temptation to reify propositions (cf. PI §22(c), §363). (ii) The idea correlative to the thesis of a common descriptive content is that assertions, assumptions, questions, requests, orders, etc. are differentiated only by reference to speakers’ attitudes towards the descriptive content. So it may seem that what differentiates an assertion from a command or a question is that, in the ﬁrst case, the speaker believes the proposition expressed by the descriptive content, in the second he wants that proposition to be made true, and in the third he wonders (or wants to know) whether it is true. Accordingly, believing, wanting, wondering are conceived to be propositional attitudes (this misleading phrase is Russell’s), i.e. attitudes towards propositions. This erroneously suggests that such verbs signify binary relations between a

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person and a proposition. And that in turn again fosters the reiﬁcation of propositions.7 But to believe that p is not the same as to believe the proposition that p, otherwise one could never believe what is in fact the case or believe what someone else knows, supposes or fears (since to know that p is not the same as knowing the proposition that p, and to suppose or fear that p is not to suppose or fear the proposition that p).

4. Sentences as instruments ‘Look at the sentence as an instrument’, Wittgenstein suggested, ‘and at its sense as its employment’ (PI §421). The analogy appealed to him, since it serves to highlight aspects of meaning, use, explanation and understanding. The meaning of a sentence, like that of a word or a phrase, is internally related to the criteria for understanding it. These are of three main types: (i) (ii) (iii)

explaining what it means, and, in the case of its use on an occasion, explaining what was said by its use; using it correctly; responding appropriately to its utterance (and, when asked, explaining or justifying one’s response appropriately).

We should note that Wittgenstein does not explicitly draw the distinction between the meaning of a sentence and what is said by the use of the sentence on a given occasion. He makes the word ‘Satz’ do far more work than a single term comfortably can do, although one must admit that what he has in mind is almost always perfectly clear. Nevertheless, we should distinguish (minimally) between the meaning of a type-sentence, what is said by the use of a sentence on an occasion (what statement is made, what order is given, what request is made, what question is asked, etc.), and what the speaker meant by the sentence he used on the occasion in question. The form of explanation typical for sentences and their uses on an occasion is paraphrase: the sentence or utterance to be explained is replaced by another sentence that dispenses with a problematic expression, an opaque construction or an uncertain use. (Note that it is not a necessary condition for a paraphrase to manifest understanding of what was said that it be synonymous with the original sentence.) If a person utters a sentence, he may be called upon to explain what he meant. If he cannot say what he meant, then there is good reason for thinking that he does not know what he was saying and was just mouthing words. If a person hears a sentence uttered, and understands what was thereby said, his response will typically be matched to what he understood. For, in appropriate circumstances, he will take the content or fact of 7

Or encourages the nominalist error of supposing that to believe that p is to believe a sentence.

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the utterance (or both) as reasons for responding as he does. Giving those reasons commonly functions as a criterion of understanding. So the different kinds of criteria are systematically interwoven. One point of stressing that speaking a language is part of a pattern of activity is that how people react to utterances manifests whether and how they understand them. Whether the assistant in language-games (2) or (8) understands the builder is to be seen from what he does; what mental processes accompany what he does are typically irrelevant. Features of the use of language are emphasized by conceiving of sentences as instruments. How we use sentences in discourse with others and how we respond to sentences when uttered by others manifest how we understand what is said. To combat the conception that speaking consists in conveying thoughts from one person’s mind to another’s (PI §363), Wittgenstein offers a fruitful analogy: speaking is akin to the activity of playing a game. Using sentences for the various purposes of discourse consists in making and reacting to moves in the language-game, i.e. in producing and responding to utterances of sentences. To use a sentence to assert or to order, etc., presupposes mastery of techniques: namely, of the language-games of assertion, command, etc. So too does understanding these uses of sentences. Only by means of a sentence (including one-word sentences) can a person make a move in the languagegame8 (PI §49), and understanding or meaning something by a sentence presupposes mastery of the relevant language-game (cf. PI §199). This conception of understanding sentences in use is parallel to Wittgenstein’s conception of understanding words. Understanding a word (knowing what it means) is a matter of knowing how to use it correctly, i.e. of having a mastery of its use. Using it correctly is a criterion of understanding it. Similarly, understanding a type-sentence is a matter of having grasped what it can be used to say, and using it correctly is a criterion of understanding it. In view of this parallelism, that the meaning of a word is its use in the language (PI §43) has as its (rather inaccurate or crude) counterpart that the sense of a sentence is its use (PI §421) or its role in the language (cf. PG 130; BB 42; PI §§21, 199). The comparison of sentences with instruments crystallizes Wittgenstein’s outlook on language in three respects. (i) It uniﬁes his objections to the Augustinian conception of language and to the descriptivist conception of sentence-meaning that can be associated with it. (ii) The dictum that the sense of a sentence is its use gives a synopsis of Wittgenstein’s tactics in dealing with speciﬁc problems about understanding sentences. In particular, he treats identity and difference in use as criteria for identity and difference of sense. Close similarity in their uses justiﬁes saying that ‘I believe that it’s going to rain’ is similar in meaning to ‘It’s going to rain’ (PI p. 190/162) and ‘He says it will rain’ to ‘He believes it will rain’ (PI 8

A slight exaggeration, given the use of words in calling someone by their name (‘Jack’), greeting a person (‘Hello’, ‘Hi’), or the use of one-word expletives that are not one-word sentences.

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p. 192/164). We might even say that the sentence ‘He can continue the series 1, 5, 11, 19, 29 . . .’ in certain circumstances has the same meaning as ‘He knows the formula an = n2 + n − 1’, because here they have the same use (BB 115). Conversely, ‘Human beings believe that twice two is four’ and ‘Twice two is four’ do not have the same sense because they have entirely different uses (PI p. 226/192f.). Wittgenstein treats lack of clear use as a criterion for denying a clear sense to a sentence (or to a picture). The questions ‘Is the visual image of a tree simple or composite?’ and ‘What are its simple component parts?’ have no clear use, i.e. no clear sense (PI §47). The sentences ‘Men have souls’ and ‘Consciousness awakens at a particular level in the evolution of the higher animals and men’ have no clear sense because the pictures that they depict have no clear applications (cf. PI §422, p. 184/157). Misapprehensions about the sense of a sentence amount to misapprehensions of its use. (iii) The comparison of a sentence to an instrument, and its use to the use of a tool, provide an analogy in terms of which to view the relation between the form and use of sentences. The analogy between words and tools was invoked by Wittgenstein to emphasize the fact that words of a given syntactical category (form) may have different uses, and that it is the latter, not the former, which must be grasped in order to comprehend correctly the notion of the meaning of a word. The same analogy serves a comparable purpose in respect of sentences. The use of an instrument is not a part of the instrument, and there is no such thing as incorporating its use into the instrument. Of course, one can stipulate that certain tools be used only for such-and-such purposes, and prohibit their use for other purposes. One may even stick labels on tools saying what uses are authorized. So too with sentences. Their form may (indeed typically does) indicate their standard use. Declarative sentences are typically used assertorically, imperative sentences to order, request or plead, and interrogative sentences to query. The form signals a typical discourse-function. But it only signals it — it does not guarantee it. In many cases, the form of a sentence (like the syntactical category of a word) may be wholly misleading with respect to its use. Arithmetical sentences have the form of assertions that something is so, but this is misleading, since their role is normative. First-person psychological sentences have the form of descriptions of states of affairs, but misleadingly so — since their role is often expressive. Grammatical propositions (e.g. ‘Black is darker than white’) look like descriptions, but are in fact expressions of rules. And so on. Furthermore, sentence-tokens of the same type-sentence may, in varying circumstances, be used very differently (e.g. ‘This is red’ may be a description of an object or an ostensive deﬁnition of a colourword). We can embody explicit markers of use in sentences, as we do with performatives verbs, but even this does not guarantee the use of the sentence (cf. the frequentative use of ‘I promise’). No matter how we ‘improve’ the form of a sentence (e.g. by paraphrase into a canonical form of mood-operator plus sentence-radical), its use on a particular occasion does not follow from its form. This has two important corollaries. (a) The classiﬁcation of sentences as

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assertions, commands, questions, etc. is a classiﬁcation of uses, not of forms. (b) Understanding an utterance implies mastery of the practice in which this sentence is used as an instrument. However, the remark ‘Look at the sentence as an instrument, and at its sense as its employment’ (PI §421) is problematic. First, characterizing a sentence as an instrument is more questionable than comparing words with tools. Instruments, like tools, are typically employed not just on a single occasion, but repeatedly. Although some sentences are used on many occasions, many are not; there is no practice of using tokens of many typical type-sentences. This does not, however, undermine the point of Wittgenstein’s analogy. Calling a sentence an instrument is intended merely to emphasize its role in a languagegame — the way its use is woven into a whole pattern of activity. Speaking is not typically an idle exercise, but is undertaken for particular purposes. Orders, threats, questions, even descriptions, are addressed to an audience to bring about or modify responses, verbal and non-verbal. The analogy with an instrument is not a bad one, and may serve as an antidote to certain misconceptions. Secondly, identifying or associating the sense of a sentence with its use is as clear and distinct as the notion of use itself, i.e. not very clear or distinct at all. Typically it is the context that shows what Wittgenstein has in mind and to what similarities and contrasts he wishes to draw attention. As noted above, we should distinguish explicitly, as Wittgenstein does not, between the meaning of a sentence, what is said, asked, ordered, etc. by its use on a particular occasion, and what the speaker meant (which may not coincide with what he said). To compare a sentence with an instrument is merely to draw an analogy. That it limps in certain respects does not prevent it from being illuminating in others. In particular, the analogy draws attention to aspects of uses of sentences obscured by insisting that the essence of a sentence is to describe. It forces us to attend to the relation between the form of a sentence and its use. It focuses upon the complexity of the criteria for understanding sentences and what is said by their use. It highlights the integration of the uses of sentences into the activities of language-users.

4. Assertions, questions, commands make contact in language The various misleading temptations scrutinized above arise not merely because of the ready surveyability of form as opposed to use, nor simply because of our natural inclination to impose a Procrustean uniformity upon dissimilar phenomena. Rather, these reasons seem to be vindicated by the fact that the distinctions they lead to appear fruitful in resolving philosophical problems. Postulation of a common content, the ‘assumption’ or ‘thought’, was intertwined with a mentalist interpretation of the acts of asserting, questioning, commanding, etc. The difference between asserting and supposing, according

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ⳕ

ⳕ

to this view, consists in the different mental attitudes towards a proposition. Accordingly, the reason why a parrot’s uttering ‘p’ is not an assertion that p is that the parrot does not perform the mental act of judging the thought that p to be true. But this is a mythology of mental acts. A person’s utterance constitutes an assertion, not because of an accompanying mental act, but because it is a use of an appropriate sentence in appropriate circumstances by a person who has mastered a practice and is familiar with the language-game in which this technique is at home. The parrot’s utterance is not an assertion; but not because it does not accompany its squawks with acts of judgement, rather because it does not play this, or any other, language-game (PI §§25, 344). It is, of course, true that uttering a sentence ‘p’ is not the same as asserting that p. But it does not follow that asserting that p involves doing something more than uttering the sentence ‘p’ — for example, judging. It is not a hidden accompaniment of the spoken sentence that determines whether it is an assertion, but the circumstances of its use and facts about its user. This point can be highlighted by means of the analogy between a sentence and a picture. A picture on its own does not tell us whether it represents what happened, what ought to have happened, what will happen, what was dreamt or wished. But no mental supplementation will make a picture reveal its secrets. It is rather the way a picture is used, in appropriate circumstances (e.g. as an illustration in a story book as opposed to an instruction manual), that renders it the representation that it is (B i §209). It seemed to Frege that we must recognize the existence of an abstract entity, the thought or assumption, in order to provide for the possibility of entertaining, supposing or hypothesizing a thought without asserting it. But that is wrong. We express a supposition or hypothesis that p with sentences such as ‘Suppose that p were the case, then . . .’, or ‘If p were the case, then . . .’. A criterion (although not the only criterion) for wondering whether p is saying ‘I wonder whether p’ or asking ‘Is it the case that p?’ Of course, what A supposes to be so may be identical with what B asserts to be so. But this does not require postulating a common object (an assumption, thought or proposition) to which the two people are differently related (see below). It might be thought that unless we postulate abstract entities expressed by sentences, and introduce explicit mood-operators signifying force, we cannot explain the non-triviality of inference by modus ponens, the possibility of negation, and other logical operations. So it might be argued that if ‘p’ means the same both times in ‘m; if m then p; therefore p’, it seems that there is no inference, for the assertion ‘p’ is already part of the premisses. If it does not mean the same, then the inference is invalidated by the ambiguity of ‘p’. But introducing a force-indicator, viz. the assertion-sign, to mark the distinction between the content and the act of assertion clears this muddle up. The content asserted in the conclusion ‘ p’ occurs also in the premiss ‘ (if m then p)’, but is not there asserted. Of course, this distinction between force and content generates new problems. What, in ordinary language, carries assertive force?

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ⳕ

How should assertoric, interrogative, imperative, etc. force be distributed among the constituents of molecular sentences? Nevertheless, we think, the ﬁrst steps towards the light have been taken. The remaining problems are merely technical. In fact, the very ﬁrst step already contained the error from which the problems ﬂow. The error is the failure to realize that to assert, to question, or command, etc. are uses of sentences. The attempt to embed the use of a symbol in the symbol used is absurd, as is patent in Frege’s remarks that his assertion-sign asserts something (FC 21, n. 7), that it contains the act of assertion (BLA i §5). But a sign is not a use, and no sign can contain its use. Of course, there are markers of use in language, e.g. the mood of the verb, the explicit performative, intonation-contours, question-marks. Although we could introduce further markers of use as preﬁxes to sentences (PI §22), such markers are neither necessary nor sufﬁcient for a given use of a sentence to be of a particular kind. It is an illusion that without a special assertion-sign we cannot explain the non-triviality of modus ponens. Of course, the two occurrences of ‘the grass will grow’ in the argument ‘If it is raining, the grass will grow; it is raining; therefore, the grass will grow’ have the same meaning in so far as an explanation of the meaning of the one will serve equally well for the other, though this will be only a partial explanation of the conditional sentence. Equally obviously, the ﬁrst occurrence of this sentence in the argument is not uttered assertively; i.e. in saying ‘If it is raining, the grass will grow’, one is not asserting that the grass will grow. One is using the molecular sentence to assert a conditional. Puzzlement about modus ponens can be cleared up only by clarifying the criteria for making an assertion. The assertion-sign can at most have the role of marking a distinction with which we are already familiar (PI §22(c)– (d)). This redundancy of the assertion-sign is apparent from philosophers’ prohibition on placing ‘ ’ in the antecedent of an asserted conditional. The reason for this, of course, is that the antecedent is not asserted. But, impeccable argument though this is, it makes grasping the differentiation of what is asserted from what is not asserted a pre-condition for mastering the correct use of the assertion-sign. If the assertion-sign were indispensable for explaining the non-triviality of modus ponens, then we would not be able to understand this explanation. The thesis that every sentence ‘contains’ (expresses) a descriptive content is appealing. It seems to lay bare the essence of sentences, and apparently explains the nature of puzzling internal relations. It must be possible, Frege insisted, for two people to believe the same thing, so what is believed cannot be an idea, which he held is subjective, i.e. identity-dependent on its owner, but must rather be something objective. This objective entity must also be something to which various people can stand in different relations, for what A believes may be identical with what B supposes, conjectures or entertains. Moreover, although what A believes may be identical with what B supposes and C conjectures, A does not believe, B does not suppose, and C does not conjecture,

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a sentence. But this seems readily explained by supposing each sentence to have as its sense a descriptive content which is what is severally entertained, supposed, believed or conjectured. Similarly, what A asserts may be identical with what B asserts, even though they do not utter the same sentence. So what they assert must be something else, i.e. an ‘assumption’ (PI §22(a)). Finally, what A orders B to do is precisely what B does when he obeys A’s order, and also precisely what B does not do if he disobeys. What B queries when he asks whether p seems to be exactly what A asserts when he answers that p, and also what he denies when he answers that not-p. These internal relations are made perspicuous, it seems, when we realize that A’s command to B has the same content (hence can be expressed by the same sentence-radical but with a different mood-operator) as the assertion that describes B’s fulﬁlment of the command, and differs from the description of B’s non-fulﬁlment of the command only in that the latter sentence-radical is the negation of the former. Similarly, a sentence-question contains the same descriptive content as its afﬁrmative answer, only it asks whether that is how things are and its answer asserts that that is how things are. It is, of course, true that what several people believe when they believe the same thing is not a private object; also, that believing, wondering, supposing are not (except trivially) relations between a person and a sentence; and that the relation between a command and its fulﬁlment is internal. But it is not true that what is believed is a public abstract object, that believing is a relation between a person and an abstract object, or that the internal relation between a command and its fulﬁlment can be explained only by postulating an assumption, thought or content of judgement that is expressed by a sentence-radical shared by a canonical formulation of the command and the assertion of its fulﬁlment. Frege’s puzzle about the apparent common content of assertion, question and supposition is resolved by pointing out that assertion, question, supposition, command, etc. make contact in language, not via an extra-linguistic entity. ‘What A asserted is what B believes’ is not the assertion of an identity between the (abstract) thing which A asserted and the thing that B believes, but rather the assertion that the same answer (e.g. in the form of a that-clause) can be given to both questions ‘What did A assert?’ and ‘What does B believe?’ The connection is set up in grammar, e.g. in the conventions for indirect speech, not via a postulated extra-linguistic entity. Similarly, the command that A bring it about that p is indeed obeyed by A’s bringing it about that p. But this is simply because the command to bring it about that p just is the command that is obeyed by bringing it about that p (PLP 119). Command and its satisfaction make contact in language (cf. PI §445). No extra-linguistic entity is needed to mediate between command and what counts as its satisfaction, nor any sentence-radical to mediate between the expression of a command and the assertion of its fulﬁlment. Of course, one can paraphrase commands and descriptions of their fulﬁlment into a canonical form in which the canonical sentences do have a common

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feature. ‘Make it the case that p’ and ‘It is the case that p’ have in common the sentence ‘p’. But that does not mean that the unparaphrased command addressed to N, ‘Go home!’, and the description of its fulﬁlment, namely, ‘N went home’, have anything in common (apart from the word ‘home’). Pari passu, if there is any common object to the question ‘Is it the case that p?’ and the assertion ‘It is the case that p’, it is merely the humble sentence ‘p’ that occurs in both (BT 206; Z §684; PI §22, see Exg.). Of course, not even this is necessary (e.g. ‘Did N go to London?’, ‘Indeed, he went home’). But the absence of a common sentential component does not imply the presence of a common nonsentential component. For each of these various puzzles Wittgenstein’s strategy of focusing upon the uses of sentences undermines philosophical theories erected to explain how we can, mysteriously, do many of the mundane things we do with language. It dissolves the mystery by clarifying the grammatical articulations that gave rise to the impression of mystery.

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

V Ostensive deﬁnition and its ramiﬁcations 1. Connecting language and reality A natural extension of Augustine’s picture of language is the idea that ostensive deﬁnition is the means whereby language is connected with reality (‘The Augustinian conception of language’, sects 1–2). If one thinks that the essence of words is to name things, and that naming is correlating a word with the thing it means, then it is natural to suppose that the mechanism whereby simple indeﬁnable names are thus correlated with their meanings is ostensive deﬁnition. Naming is conceived to be the foundation of language, and ostensive deﬁnition appears to be the point at which, as it were, we exit language (WWK 246). By ostensively deﬁning a simple name, we link it to an entity (an object, in a generous sense of the term) in reality. That entity is what the word thus deﬁned stands for, it is what the name means — it is the meaning of the name. It is in virtue of such word–world links that the web of language has a content, and it is by reference to them that we explain what indeﬁnables mean. It is noteworthy that in the work of the young Wittgenstein there is no such conception of ostensive deﬁnition. Of course, the term ‘ostensive deﬁnition’ had not yet been invented (see ‘The Augustinian conception of language’, sect. 2)). But that is not the point. Rather, there was in the Tractatus no conception of a form of deﬁnition or explanation of word-meaning which linked indeﬁnable simple names to their meanings. Nevertheless, in 1932 Wittgenstein remarked to Waismann, ‘In the Tractatus logical analysis and ostensive deﬁnition were unclear to me. At that time I thought that there was a “connection between language and reality” ’(WWK 209f.). What did he mean by this? It is evident that in the Tractatus the method of projection was conceived to be an act or activity of meaning by the sentence in use such-and-such a situation, i.e. its sense (see ‘Turning the examination around: the recantation of a metaphysician’, pp. 255f.; PT 3.1–3.15, TLP 3.11, MS 108 (Vol. III), 219; MS 116 (Vol. XII), 275); and by the constituent words in a given sentence, the speaker was held to mean the correlative objects that are their meanings. This does not resolve the question of how names, in particular, how indeﬁnables are to be explained. Wittgenstein asserted that they are explained by elucidations or clariﬁcations (Erläuterungen). ‘Elucidations’, he declared, ‘are

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propositions that contain the primitive signs. So they can be understood only if the meanings of the signs are already known’ (TLP 3.263). The idea is not as obscure as it seems. In fact, it is similar to Russell’s account of the explanation of primitive signs in Principia *1: ‘The primitive ideas are explained by means of descriptions intended to point out to the reader what is meant; but the explanations do not constitute deﬁnitions because they really involve the ideas they explain.’ The simplest case of such explanations, it seemed, is a sentence of the form ‘This is A’, which describes this as being A, and is true if it is. The elucidation connects language to reality by saying of a given object that it is A. It is intended to convey to the hearer what is meant by ‘A’, but, of course, it will be understood as a true predication of ‘A’ only if one gathers what ‘A’ means. It was only in 1929 that it occurred to Wittgenstein that he had conﬂated two quite distinct roles which sentences of this form can play. In Philosophical Remarks, he wrote: If I explain the meaning of the word ‘A’ to someone by pointing to something and saying ‘This is A’, then this proposition may be meant in two different ways. Either it is itself a proposition already, in which case it can be understood only once the meaning of ‘A’ is known, i.e. I must now leave it to chance whether he takes it as I meant it or not. Or the sentence is a deﬁnition.1 (PR §6)

The Tractatus conception of ‘a connection between language and reality’ was awry. We do indeed explain certain ‘primitive signs’ perfectly decently. But they are not explained by ‘elucidations’ consisting of empirical propositions such as ‘This is A’, which are applications of ‘A’ and which leave it to chance whether the hearer will gather what is meant.2 Rather, they are explained by means of ostensive deﬁnitions. Such explanations are not true or false predications, but give a rule for the use of the deﬁniendum ‘A’. The object pointed at is typically a deﬁning sample. It is not the meaning of the deﬁniendum (meanings of words are not objects of any kind). Nor is it described by the ostensive deﬁnition. It is a constituent of the rule — i.e. of the ostensive deﬁnition — that speciﬁes the meaning of the deﬁniendum. The deﬁning sample belongs to the means of representation, and not to what is represented. So ostensive deﬁnitions do not link words and world, but remain within language. ‘I cannot use language to get outside language’ (PR §6) — there is no ‘exit’. This radical conception will be explained below. It is no surprise that in the early 1930s Wittgenstein spent so much effort clarifying the nature and status of ostensive deﬁnition and was furious when 1

Compare TLP 3.263: ‘Sie können also nur verstanden werden, wenn die Bedeutungen dieser Zeichen bereits bekannnt sind’ with PR §6: ‘. . . kann dann erst verstanden werden, wenn die Bedeutung von A bereits bekannt ist’. 2 Of course, that does not mean that someone may not gather what ‘A’ means from such applications of A (cf. PI, p. 18/16, paragraph b).

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he thought that Carnap had published his advances on this subject without due acknowledgment.3 For it was now clear that misconceptions of ostensive deﬁnition can wreak havoc with one’s picture of the relationships between language and what it represents.

2. The range and limits of ostensive explanations Wittgenstein emphasizes the possibility of using ostensive deﬁnitions to explain a wide range of expressions. These include colour-names (e.g. ‘red’, ‘violet’), proper names of persons or things (e.g. ‘N.N.’, ‘Mont Blanc’), names of stuffs (e.g. ‘sugar’, ‘iron’), of shapes (e.g. ‘cube’, ‘arch’), of kinds or species (e.g. ‘dog’, ‘chair’), verbs (e.g. ‘digging’, ‘lifting’) and even number-words and logical operators (e.g. ‘two’, ‘not’). Giving ostensive deﬁnitions of such expressions correctly explains what they mean. Ostensive deﬁnition is not restricted to so-called indeﬁnables. Pointing at a tennis ball and saying ‘That is spherical’ is a correct explanation of ‘spherical’, even though it is possible to give a lexical, analytic deﬁnition of the word. That a lexical deﬁnition is available does not imply that an ostensive deﬁnition is illicit or inferior. Over a wide range, ostensive explanations are equipollent with various forms of lexical explanations, including analytic deﬁnitions. Wittgenstein does not aim to show that ostensive deﬁnitions are defective by comparison with other forms of explanations of meaning. On the contrary, his purpose is to prove that they are not especially privileged; in particular, that they do not lay the foundations of language. Ostensive deﬁnition is demoted to the ranks, not cashiered. It is a legitimate way of explaining the meanings of many expressions. In emphasizing its wide competence, Wittgenstein also challenges the idea that there are kinds of words, e.g. all number-words, names of points of the compass (PI §28), logical connectives (PG 61; PLP 105), that cannot be deﬁned ostensively. One might think that number-words are second-level predicates or names of ‘abstract entities’; they do not stand for something perceptible, and that is why they cannot be explained by ostension. One might claim that directions can be referred to only by a complex singular term formed from an operator ‘the direction of . . .’ applied to a singular term designating a line; hence, too, that understanding the name of a direction presupposes understanding this functional expression and the argument-names it takes. So directions, such as ‘north’, cannot be deﬁned ostensively. In the case of logical connectives, it seems that there is simply nothing to point to in explaining them. 3

See Wittgenstein’s letter to Schlick, 8 August 1932, in which he remonstrated against what he saw as plagiarism. It included the following (my translation): ‘I don’t believe that Carnap no longer remembers the conversations with Waismann, in which the latter told him of my conception of ostensive deﬁnition’ (see M. Nedo and M. Ranchetti eds, Wittgenstein, Sein Leben in Bildern und Texten (Suhrkamp, Frankfurt am Main, 1983), p. 255).

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Wittgenstein insists that we do accept as perfectly exact an explanation of ‘two’, e.g. by pointing at a pair of nuts and saying ‘That is called “two” ’ (or ‘The number of these is two’). What must be removed are the obstacles to accepting such an explanation at its face value. One objection is that an ostensive explanation of ‘two’ might be misinterpreted, e.g. as a proper name of this particular pair of nuts. To this there are two ripostes. First, every ostensive deﬁnition is open to misinterpretation (PI §28), and so indeed is every explanation of whatever form (PI §87); hence, this objection has no special relevance to whether certain number-words can be ostensively deﬁned. Secondly, what can be misinterpreted need not be misinterpreted; a person may well learn how to use ‘two’ correctly from this ostensive explanation, and whether he does so will be manifested by his subsequent applications of ‘two’. An explanation, including an ostensive one, is correct provided that giving it is accepted as a criterion of understanding the expression it explains (PI §87). A second objection is that number-words stand for abstract entities or secondlevel concepts that cannot be pointed at. But now one is being misled by the conception of meaning as naming. To say that a number-word is the name of a number (or of an abstract entity) merely invokes a form of representation (‘the word . . . signiﬁes . . .’; cf. Exg. §§9f., 13) which is at best empty, at worst misleading. First, it imposes a spurious uniformity on a range of logically heterogeneous number-words and numerals (e.g. ‘2’, ‘ 1/2’, ‘0.5’, ‘0.333 . . .’, ‘√2’, ‘π’, ‘2 + 2i’, ‘π′’). Secondly, treating number-words as names of secondorder properties obscures the important differences between number-words and expressions of generality (e.g. between ‘three’ and ‘there is . . .’). What must be grasped in understanding number-words or numerals is their use, not their meanings conceived of as entities which, by artiﬁcial manipulations of formal concepts, one can represent them as ‘standing for’. Therefore, there is no reason why ostensive deﬁnitions should not explain the names of the initial numbers in the sequence of cardinals.4 And it is noteworthy that the category of the expression explained by ostension is shown by the accompanying training (e.g. memorizing the number-series and learning to carry through 1:1 correlations), not by supplementary explanations employing formal concepts (e.g. of a second-level predicate) (BB 79). Parallel responses are appropriate to the objections that directions and logical connectives cannot be deﬁned ostensively. ‘North’ is readily explained by using a compass (or the north star) and pointing and saying ‘That is north’. Understanding ‘north’ does not require knowledge of how to use the functional expression ‘the direction of ’, but only being able to apply ‘north’ correctly; e.g. understanding is manifested by obeying the order to go north or 4

Waismann noted that the fact that the ﬁrst four numerals are declined in Greek seems to indicate that a difference was felt between the numbers that can be taken in at a glance (and can therefore be ostensively explained) and the others. One might accordingly distinguish between ‘visual number’ and ‘inductive number’ (PLP 105).

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by giving a correct answer to the question whether some person went north. Similarly, Wittgenstein asserts that one can explain the use of ‘and’, ‘not’ and ‘or’ by gestures: ‘and’ by a gesture of gathering together (BT 42; PG 53), ‘not’ by a gesture of rejection or exclusion (BT 34, 42; PG 58, 64; PI §550), and ‘or’ by presenting alternative choices in a gesture (PLP 105). One might ostensively explain negation, e.g., by saying ‘No more sugar’ and taking the sugar away (PG 64), or by drawing a ﬁgure and saying ‘Look, this point is in the circle, that one is not’ (PLP 105). Explaining ‘not’ by gestures is no more problematic than explaining it by a truth-table, for that too is simply a pattern of signs whose meaning lies in its use, and this use is analogous to the use of the gesture of rejection or denial (PG 55, 58). The range of expressions ostensively deﬁnable is much wider than philosophers have recognized. One might object that Wittgenstein reaches this conclusion only by distorting the concept of ostensive deﬁnition. Does the possibility of explaining negation by a gesture of exclusion, for example, show that the word ‘not’ can be given an ostensive deﬁnition? Although there is some justice in this objection, nevertheless it misrepresents the concept of ostensive deﬁnition. The boundaries of this concept are ﬂuid (PLP 104ff.). There is a range of paradigmatic examples of ostensive deﬁnitions, and surrounding these are many explanations differing in various ways from the central cases. The class of ostensive deﬁnitions merges imperceptibly into explanations of different forms that might, for certain purposes, be treated as distinct. No gulf separates ostensive deﬁnitions from analytic deﬁnitions; there is a continuous spectrum of connecting links. Provided this is acknowledged, where the boundary of ostensive deﬁnition is drawn matters little. Central cases of ostensive explanations involve three elements: (i) a deictic gesture, (ii) something pointed at, and (iii) a verbal formula (e.g. ‘That is . . .’ or ‘That is called “. . .” ’). Among them would be the explanation of ‘red’ by pointing at a red book and saying ‘That is red’, of ‘metre’ by pointing at a metre stick and saying ‘The length of this is one metre’, of ‘dog’ by pointing at a bull-dog and saying ‘That is a dog’, and of ‘N.N.’ (or of who N.N. is) by pointing at someone and saying ‘He is N.N.’. These paradigms resemble each other in many respects. These resemblances become fewer and more attenuated as we move away from the central cluster towards peripheral cases. (i) What counts as a deictic gesture? Clearly one can point to a colour patch, a dog, some nuts or a point of the compass. But can one point to a sound or a smell? One can call attention to a tone with a gesture; e.g. one might say, ‘Listen, that is C ﬂat’, indicating a particular note by jerking one’s extended index ﬁnger or pointing in the direction from which the sound is coming (PLP 104f.). One might say, ‘Smell, this is putrid’, having something that smells putrid on the end of one’s index ﬁnger and putting this under another’s nose. The limits of what counts as pointing are unclear (and perhaps unimportant). The explanation of an olfactory or tactile property by means of a sample seems essentially parallel to the explanation of a colour-word. Indeed,

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we might let pointing drop out of consideration altogether and count as a form of ostensive deﬁnition an explanation of colour-words or shape-words by means of a chart correlating words and samples or pictures (PLP 107f.). (ii) What counts as something pointed at? Clearly one can point at a particular object, but can one point at its colour, shape, texture, weight, length or number? Can one point at (as opposed to in) a direction, an action (e.g. lifting a weight) or an activity (e.g. playing football)? The gesture of pointing here is clear-cut, but not so what is pointed at. Of course, we contrast pointing to the colour of a book with pointing to its shape. But in both cases is not the book what we really point to, though in the ﬁrst we use it as a sample for explaining a colour-word and in the second as a sample for explaining a shape-word? The parallel treatment of directions, actions and activities seems impossible. When one points to the north, does this mean that one is really pointing to some object, say a tree on the horizon, which one is using as a sample of north? An alternative account might exploit the greater powers of mental archery. Deixis might be replaced by the speaker’s intention, for he can certainly mean a number, a colour, a shape, a direction, an action or an activity in ostensively explaining a word. This would liberalize the range of things that can be pointed at (or to), but at the price of requiring an explanation of what it is to mean the colour rather than the shape of a book or the number rather than the conﬁguration of some nuts (cf. Exg. §§33ff.). The question is: what are the possible substitution-instances of ‘x’ in the expression ‘pointing to (at) x’. But, once formulated, this seems idle for clarifying ostensive explanation. What is crucial is the practice of explaining words such as ‘red’, ‘round’, ‘rough’, ‘one kilogram’, ‘one metre’, ‘three’, ‘north’, ‘lifting a weight’, etc. and the similarities between these kinds of explanations. (iii) What counts as an admissible form of words in an ostensive deﬁnition? The paradigm formula is ‘This is . . .’; e.g. pointing to a red patch and saying ‘This is red’. Equally appropriate would be ‘This colour is red’. But also, ‘This is called “red” ’, ‘ “Red” means this colour’ (cf. MS 114 (Vol. X) Um., 42), and ‘ “Red” means the same as “This + colour” [pointing at the red patch]’. The ﬁrst pair use the word ‘red’, and the subsequent trio mention it; but all fulﬁl the same role of explaining what ‘red’ means and providing a standard of correctness for its use. However, the boundaries of the appropriate form of words are blurred. What if one says ‘This and this and this are red’? Or ‘This is red, and that is not red’? Or ‘This is red, and anything else is red that resembles this more closely than it resembles that [a sample of orange] and that [a sample of purple]’? With many sortal nouns one could even spell out the relevant respects of resemblance: e.g. ‘This is a bearded warbler, and so too is any warbler resembling it in having a decurved bill and a broken eye-ring.’ Here, it might seem, the ostension and the specimen would drop out of the explanation altogether, since the similarity-clause amounts to a deﬁnition by genus and differentia. An explanation of ‘game’ may be given by a set of paradigms picked out ostensively. Is this an ostensive deﬁnition, an explanation by

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examples and a similarity-rider, or both? The principles for the individuation of explanations are unclear, and so too are the principles for determining of explanations complex in form whether they count as ostensive deﬁnitions. What is clear, however, is that characteristic features of paradigmatic ostensive explanations are present in varying degrees in more complex explanations, and that there are many kinds of explanations transitional between paradigmatic ostensive deﬁnitions and paradigms of other forms of explanation. These questions expose some ways5 in which ostensive deﬁnitions shade off into explanations of other types. But there are other kinds of borderline cases, for ostensive explanations also shade off into things which are not explanations at all. The vagueness of the boundary separating explanation from teaching and training (cf. ‘Explanation’, sect. 1) is apparent in the case of ostensive deﬁnition. There are primitive forms of ostensive teaching that precede ostensive deﬁnition in the order of learning (cf. Exg. §6). Where such training ceases and ostensive explanation begins is not sharply determined (PG 62). Given his purpose of examining all forms of explanation that seem to establish connections between language and reality, it is appropriate for Wittgenstein to interpret the phrase ‘ostensive deﬁnition’ as generously as he does. None the less, one might object, conceding this point does not establish his conclusion that ostensive deﬁnitions are equipollent with other forms of explanation for a wide range of expressions. Are they not comparatively inadequate? In particular, though correct, are they not typically incomplete? Of course, it is correct to explain ‘circle’, for example, by pointing to a circular object and saying ‘That is a circle’, but does not a geometrical deﬁnition (‘the locus of points equidistant from a given point’) give a fuller, better understanding of ‘circle’? Does a typical ostensive deﬁnition not yield at best only a partial understanding of what it explains? This objection runs counter to Wittgenstein’s account of explanation, and involves misconceptions about correctness and completeness (cf. ‘Explanation’, sect. 3). We count as a correct explanation of ‘red’ any ostensive deﬁnition of ‘red’ using a red object as a sample. There is no necessity that we should treat all red objects as admissible for the purpose of explaining ‘red’; but the fact that we do so is an aspect of the grammar of our language. Similarly, there is no need for us to incorporate any ostensive deﬁnitions in the practice of explaining ‘circle’; the simple fact is that we do. It seems that since my copy of the Tractatus, for example, has red covers, I must be able to use it in giving an ostensive deﬁnition of ‘red’ because I can, by pointing to it and saying ‘This is red’, correctly describe it as being red. It then seems wholly trivial that ostensive deﬁnitions are correct explanations. This is a residue of confusing explanations with applications (e.g. TLP 3.263; cf. PI p. 18/16, paragraph b), 5 There are others too. PI §9 hints at one. Suppose I explain ‘ten’ by pointing in succession to each one of a group of ten marbles while counting aloud ‘one, two, . . . ten’; have I thus given an ostensive deﬁnition of ‘ten’?

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for it appears that we must acknowledge as a correct explanation of an expression any instance of its correct application. But an application is not an explanation, and nothing forces us to adopt given practices of explanation. We do accept ostensive explanations as legitimate, and this is not a trivial feature of our linguistic practice. The possibility of misinterpreting an ostensive deﬁnition does not prove it to be incomplete. Since any explanation can be misinterpreted, this possibility does not show ostensive deﬁnition not to be equipollent with other forms of explanation. Similarly, the fact that ostensive deﬁnition presupposes stagesetting (especially knowledge of how to use the kind of expression to which the explicandum belongs) is not a proof of incompleteness. Whether an explanation is complete, i.e. provides a standard of correctness for normal cases of the application of the explanandum, is an aspect of its normative role. This cannot be seen from scrutiny of its form. Rather, it depends on whether adducing it counts, in our practices, as an adequate explanation in standard cases and as a criterion of understanding. The illusion that ostensive deﬁnitions are incomplete is supported by an unclarity about concept-identity. We are inclined to acknowledge that a geometrical deﬁnition of ‘circle’ gives a fuller understanding than an ostensive deﬁnition and, similarly, that a zoological explanation of ‘dog’ is more complete than our everyday ostensive explanations. Perhaps a better response would be that the concepts explained in geometry and zoology are different from our ordinary ones, though closely akin to them. There seems every reason to accept Wittgenstein’s contention that ostensive deﬁnitions are perfectly adequate, i.e. both correct and typically complete, for a much wider range of expressions and kinds of expressions than is commonly acknowledged.

3. The normativity of ostensive deﬁnition Ostensive deﬁnitions have a normative role in language. They guide linguistic behaviour by providing standards of correctness for the use of the expressions whose meanings they explain. Wittgenstein insists that ostensive deﬁnitions are rules (BT 176; BB 12, 90); hence that they belong to ‘grammar’, in his idiosyncratic use of this term (PR 78; PG 88; PLP 13f.). In respect of normativity, they do not differ from lexical deﬁnitions (PLP 278). One may raise two objections to this conception. (i) Is it not a distortion of the concept of a rule to assert that ‘tables, ostensive deﬁnitions, and similar instruments . . . [are] rules’ (BB 90)? It had surely never occurred to anyone to conceive of pointing at an object and saying ‘That is . . .’ as giving a rule, let alone to refer to a colour-chart as a set of rules. Wittgenstein’s retort would perhaps be that the concept of a rule is a familyresemblance concept, explained by reference to similarities with paradigmatic

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examples (cf. PLP ch. VII). Its boundaries are indeterminate (BT 67ff., 246). For the purposes of clarifying the role of ostensive deﬁnitions in our language, it is important to emphasize their similarities with lexical deﬁnitions, and hence advantageous to classify them together as rules. (ii) How is it possible to distinguish the case of following an ostensive explanation (or an explanation by a table) from behaving in accordance with it (PG 86)? How can such a rule guide behaviour? How can it enter into the applications of the explained expression? Although this is a general problem about clarifying the concept of applying rules, it seems particularly intractable in the case of ostensive deﬁnitions. Wittgenstein wrestled with it for some time, proposing a number of unsatisfactory solutions. (a) The function of an ostensive deﬁnition is to correlate a word with a mental sample (e.g. the word ‘leaf ’ with a mental image of the shape of a leaf (cf. PI §73)), and subsequent applications of the word turn on comparisons with this image. So, an ostensive deﬁnition enters into applications via a memory image. (b) Its entering into the application of a word might be thought to consist in the fact that the ostensive deﬁnition is rehearsed (or the table consulted) just prior to applying the word (BB 12 –14). (c) The ostensive deﬁnition might be deemed to enter into the application provided that it refers to a sample that is used in the process of applying the deﬁned word, e.g. as a metre stick is in metric measurement; in such cases the ostensive deﬁnition furnishes a concrete standard of comparison. None of these seems to give a correct general account of what it is to follow an ostensive explanation in applying an expression. One may be inclined to object, ‘Isn’t it like this? First of all, people use an explanation, a chart, by looking it up, later they as it were look it up in the head . . . and ﬁnally they work without the chart . . .’ (PG 85f.). And is this not parallel to the development of the way that the rules of chess typically enter into the play of a chess-player as he gains experience (PLP 129ff.)? This is partly right; and for this reason Wittgenstein came to reject these proposals. But he denied that ostensive deﬁnitions were therefore a matter of mere history (contra PG 86f.). Their connection with the applications of words is simply not made in the minds or the overt behaviour of speakers on each occasion of using these words, but in the practice of explaining (applying, and justifying the application of ) these words. Provided that Wittgenstein’s subsequent argument (PI §§185ff.) undermines the general misconception that a person follows a rule only if he consults it, the special difﬁculty of conceiving of ostensive deﬁnitions as rules disappears. Having set aside these two preliminary objections, one might wonder how it is possible for an ostensive deﬁnition to play the normative role essential to a rule. How can it function as a standard of correctness? How can applications be justiﬁed or criticized by reference to an ostensive deﬁnition? There seems to be no connection between the ostensive deﬁnition of an expression and its subsequent applications. Someone may point, for example, to one red

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object and say ‘This + is red’, and then apply the term to other objects, saying ‘That + is red’. Surely, since the objects are distinct, the correctness of what he says in the second case is a matter independent of anything uttered in the ﬁrst case. This objection turns on a misconception of ostensive deﬁnition: namely, that in saying ‘This + is red’ to explain what ‘red’ means, one is describing a particular object as being red. If that were so, then what it is correct to say about another object would be independent of what is said in the ostensive deﬁnition. But the premiss is false. The ostensive deﬁnition is not a description; rather, it explains what it is for any object to be red. That is why it is normatively related to applications of ‘red’ to objects. For, in saying in the latter case, ‘That + is red’, one means that that + (pointing at the object being described) is this + colour (pointing at the colour of the sample). None the less, it might be objected, it is still not clear how ostensive deﬁnitions provide standards of correctness. If one explains ‘red’ as the colour of this + object, then of course something is red if and only if it is the colour of this + object, but that is merely a tautology: namely, that something is red if and only if it is red. Moreover, nothing is said about how to decide whether another object is the colour of this object, and hence no provision is made for this sample of red to play any role in justifying or criticizing applications of ‘red’. So what sense is left to the claim that ostensive deﬁnitions are rules constituting standards of correctness? Matters can be illuminated by conceiving of an ostensive deﬁnition as akin to a substitution-rule. In this respect, it is not as far removed from an analytic deﬁnition as it seems to be. We can, for example, regard the deictic gesture and the sample of red as a symbol, and take the explanation ‘This + is red’ as giving a complex and partly concrete symbol interchangeable with the word ‘red’ (cf. BB 109). Instead of saying ‘The curtains are red’, one could say, ‘The curtains are this colour + (pointing at the sample)’. Of course, an ostensive deﬁnition (or a table) leading from a word to a sample, although it is similar to, is nevertheless different from, a translation-rule leading from one word to another (PG 91): for example, ‘bachelor’ = df. ‘unmarried man’. For although the word ‘red’ can always replace the complex symbol consisting of ‘this colour’, the gesture and the sample, the converse replacement may be impossible because the sample is unavailable. Furthermore, while ‘red’ can be said to be the name of a colour, one would not say that ‘This colour’, the deictic gesture and the sample collectively are the name of a colour. Finally, although the word ‘red’ is, in some sense arbitrary, and might have been used to signify the colour green, the sample of red is not thus arbitrary. It could be used (in a code, for example) to stand for green, but not as a sample of green. Now, however, one might object that viewing ostensive deﬁnitions as substitution-rules makes a sham of their justiﬁcatory role. For to say ‘That poppy is this + colour (pointing at the sample of red)’ is simply to say ‘That poppy is red’, and hence it cannot be a justiﬁcation for saying the latter.

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This objection confuses different senses of ‘justiﬁcation’. Of course, normal colour judgements are immediate and not inferences from, or warranted by, evidence. An ostensive deﬁnition of ‘red’ does not furnish a standard for showing applications of ‘red’ to be evidentially justiﬁed or unjustiﬁed in this sense. What it does is provide a standard of correctness for the use of the word ‘red’. We appeal to ostensive deﬁnitions in criticizing misapplications of ‘red’: someone might say, for example, ‘You described that + as red, but this colour is red, and that + is not this colour’. Speakers normally agree on how to deﬁne ‘red’ ostensively; they generally agree which applications of ‘red’ are correct and which not; ﬁnally, they agree that correct uses of ‘red’ accord with these ostensive deﬁnitions. There is here widespread agreement both in deﬁnitions and in judgements (PI §242). It is noteworthy, however, that not all colour predicates are like ‘red’. Our recognitional capacities are such as to enable us, in standard cases, to apply ‘red’ (or ‘green’, ‘blue’, ‘yellow’, etc.) without using a sample as a standard of comparison. At most we might make use of one under abnormal observation conditions or in the case of a disagreement with another person that might occur under non-optimal conditions. But it is not like that with respect to a multitude of names of reﬁned shades of colour, for the identiﬁcation of which mere recognitional abilities are inadequate. In these cases, we typically make use of samples in the application of the colour-word. When it comes to weights and measures, or tones, samples typically ‘enter into’ the actual application of the predicates, inasmuch as our recognitional capacities regarding lengths, weights and tones (unless we happen to have perfect pitch) are poor. The normativity of ostensive deﬁnitions is closely connected with some of Wittgenstein’s most important arguments. (i) An ostensive deﬁnition is a rule (PG 88), not a statement or a description. The sentence ‘This is red’ may be used to describe an object picked out by the demonstrative ‘this’ together with a deictic gesture, or to explain what ‘red’ means (PR 54). It cannot be used simultaneously for both purposes. Its being used as an explanation of meaning is incompatible with its being used as a description. For what is a measure (e.g. an ostensive deﬁnition of red) cannot, at the same time, be the result of a measurement (e.g. a description of an object as being red). (ii) Since an ostensive deﬁnition is a rule, Wittgenstein’s remarks about following rules apply also to ostensive deﬁnitions (and explanations by charts and tables). In particular, every ostensive deﬁnition can be misinterpreted (PI §§28, 86). Consequently, it can always be further interpreted. We may, for example, explain an ostensive gesture by words (MS 114 (Vol. X) Um., 63; PG 90) or append to a table a rule for how to read it (PI §86; PLP 149f.). Since the ostensive deﬁnition of ‘red’ does not by itself determine the network of internal relations between red and other colour determinates — for example, that red is darker than pink, that red is more like orange than it is like yellow, etc. — we may supplement it with a formulation of the rules of

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colour geometry. Similarly, since we cannot read off that ‘red’ is a colourword from the object pointed at in ostensively deﬁning ‘red’, we may supplement the ostensive deﬁnition by adding ‘Red is a colour’ or substituting ‘This colour is red’ for ‘This is red’. Rules can always be devised to guide the application of a given rule, and in some circumstances various such supplementations may be required to avert misinterpretations or misunderstandings. So we might say that any ostensive deﬁnition is only one rule among many that jointly guide the use of an expression (PG 61; PLP 61–8). Equally, we might claim that understanding an ostensive deﬁnition presupposes knowledge of the grammatical post at which the deﬁniendum is stationed (PG 88; PI §§29–31). But neither of these observations should be taken to imply that an ostensive deﬁnition by itself is a mere Ersatz explanation. (iii) An ostensive deﬁnition should not be regarded as forging a connection between language and reality (PG 89; PLP 277–9). That misconception is part of the Augustinian conception of language. It confuses the fact that with an ostensive deﬁnition we step outside word-language into gesture-language with the illusion that we are making a ‘connection between language and reality’ (cf. MS 114 (Vol. X) Um., 59). It confuses a sample that belongs to the means of representation with an object to be represented (hence the muddle of the Tractatus conception of ‘elucidation’). It fosters the misguided idea that grammar reﬂects the essential natures of the objects correlated with expressions by ostensive deﬁnitions, as if combinatorial possibilities and internal relations ﬂowed from the natures of these objects. Finally, it suggests that no ostensive deﬁnition can be further interpreted because it reaches right up to the object that is the meaning of the explicandum. But ostensive deﬁnitions do not ‘connect words with the world’. They explain words (constituents of ‘word-language’) in terms of partly concrete symbols (gesture, sample and demonstrative). So they remain within language, i.e. within the means of representation. We should count the objects employed in ostensive deﬁnitions (and explanations by tables) as samples, and ‘It . . . causes least confusion to reckon the samples among the instruments of language’ (PI §16). They belong to the ‘means of representation’ (PI §50). This is not a dogmatic claim, but rather the recommendation of a terminology for the purpose of facilitating an overview of language (PLP 277ff.). In particular, it promotes the insight that explanations explain only within language, and hence that language is ‘self-contained and autonomous’ (MS 114 (Vol. X) Um., 75; PG 97).

4. Samples Ostensive deﬁnition is bound up with the use of objects as samples. To explain what ‘red’ means by pointing to a ripe tomato and saying ‘This colour is red’ is to employ the tomato as a sample of the colour red. To be sure, not every ostensive deﬁnition makes use of objects as samples — as noted above,

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an ostensive explanation of ‘north’ does not. Conversely, it would be misleading to treat every case of explanation by means of a sample as an ostensive deﬁnition, even under a generous interpretation of ‘ostensive deﬁnition’. Stretching the notion of pointing accommodates explanations by charts or tables and explanations by exempliﬁcation of tastes, sounds or smells; but not even that allows inclusion of explanations by samples that are described or located such as ‘Red is the colour of the stain on my carpet’, ‘Red is the colour of fresh blood’, or ‘One metre is the length of the standard metre in Paris’. It would be better to distinguish ostensive deﬁnitions by means of samples as a species within the genus of explanation by samples. ‘Sample’ is one of a family of words, which includes ‘type’, ‘specimen’, ‘pattern’, ‘model’, ‘example’, ‘paradigm’, ‘exemplar’, ‘archetype’, ‘standard’ and ‘prototype’. Although their uses are akin, they are distinguishable. A request to see specimens of Wilton broadloom carpets, for example, is quite different from a request to see samples of such carpets. Wittgenstein’s term is ‘Muster’ or ‘Paradigma’. ‘Sample’ captures the idea that what is characterized as ‘ein Muster’ represents something, and also captures the normative aura of ‘Muster’, i.e. being usable as a standard of comparison. ‘Paradigm’, ‘exemplar’ and sometimes ‘pattern’ or ‘specimen’ are other possible translations. Rather than exploring any subtle differences between these, the term ‘sample’ will be used throughout, with awareness that its boundaries are ﬂuid. Central cases of its application are familiar: samples of cloth, colour-charts, samples of sodium chloride, museum specimens such as bird skins or fossils, patterns to be copied such as a spandrel from an antique clock, actions or activities enacted as authoritative examples to be followed by others, or species used to typify genera in a schema of biological classiﬁcation. Five features of samples are noteworthy. (i) The range of samples in general is wide and heterogeneous. The range of samples used in ostensive deﬁnitions is constrained primarily by the requirements consequent upon the use of samples as standards of correctness for the employment of a word and (when necessary) as objects of comparison. (ii) The status of something as a sample depends on how it is used. One might, for example, take a sample of carpet from a sample-book in a shop and use it to carpet the ﬂoor of a doll’s house. Then it would no longer be a carpet sample.6 Conversely, one might take a dinner service in use for many years and put it in a museum as a specimen of a particular type of china. It would then become a sample, which it had not been before. So too, something used as a sample in an ostensive deﬁnition may subsequently lose its role. (iii) A single object may have multiple uses as a sample. A particular swatch of cloth might be used one day as a sample for a colour, another day as a sample for a weave or kind of fabric. Alternatively, it might be used simultaneously, rather than successively, as a sample for several different things. So, as we shall see, a sample of white in an ostensive deﬁnition, in conjunction with 6

This example is due to Professor W. Künne.

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a sample of any other colour, is also usable simultaneously as a sample of the relation of being lighter than. To call something a sample is to characterize its role, not its intrinsic features. (iv) When used as samples, functional objects typically do not have their usual functions, or actions their standard roles. A sample set of china, for example, sits unused in a shop window, and wallpaper samples are found in samplebooks instead of being used to decorate a room. Similarly, a musician demonstrating how to play ornaments in Bach’s Forty-eight is not playing a fugue, and a joiner showing how to cut a mortice may not be making a component of a piece of furniture. (v) Samples enter into human activities and transactions in various ways. One might enclose a sample of a colour in a letter if one wanted to order material of that colour; the sample would be part of the order (PR 73). Similarly, oral orders might be accompanied by exhibiting appropriate samples, for example, of colours (cf. PI §8) or sounds (PI §16). Somebody asked to fetch a bolt of cloth matching a sample in colour might take the sample with him and hold it against each bolt of cloth to judge match or mismatch; he might leave the sample behind and invoke a memory image of it; or he might simply go off without the sample and come back with the correct material (BB 84ff.). Museum specimens might be used to categorize dead animals, to examine the ability of students at zoological classiﬁcation, or to standardize the terminology of classiﬁcation. A sample of water from the Thames might be subjected to chemical analysis and used to formulate ecological policies. Such possibilities can be multiplied indeﬁnitely. Further clariﬁcation of the concept of a sample can be derived from examining the resemblances that bind together the various things classiﬁed as samples. First, a sample represents that of which it is a sample. Hence, it must belong to and be typical of the whole or kind which it represents. We may not use a class in a primary school as a sample of the British electorate, a stork as a sample of an elephant, or a red object as a sample of green (cf. BT 49; PG 90f.). If we want to explain what the word ‘red’ means by reference to something that we use, pro tempore, as a sample, it must be red. Similarly, it must be clearly red, and not a borderline case. Likewise, a sample set of electors used in an opinion poll, for example, must be representative of the whole voting population in relevant respects (age, sex, occupation, etc.); a sample of water from the Thames must be typical of the water in a given part of the river if it is to be useful for formulating policies of pollution control on the basis of its chemical analysis; a specimen of a butterﬂy in a museum must be typical of the species to which it belongs if it is to serve as a basis for formulating a description useful for identifying members of the species. Conversely, an abnormal, deviant or atypical X may not legitimately be used as a sample of an X; a deformed stork, for example, cannot serve as a sample of a stork. These points are normative. A prediction of an opinion poll may be correct, but that does not entail that the survey group is representative of the electorate. Similarly,

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after taking a particular drug, we might all use a red object in a way similar to that in which we now use a sample of green, but that would not make it a sample of green. De facto success in the role normally discharged by a sample does not legitimate taking something to be a sample. What it is for something to be representative is not sharply circumscribed, and different standards are applied in different cases. Secondly, a sample can commonly be copied or reproduced. We can, for example, reproduce a colour sample by printing colour-charts, and we can copy it by painting a wall the same colour. Many different things, however, count as copying a sample, depending on our purposes, how we compare things with samples, and the context of the activity (PG 91f.). The copy may be on a bigger scale than the pattern (e.g. a Chippendale chair copied from the Directory), or on a smaller scale (e.g. a microcircuit in a calculator); it may be made by eye and without instruments (e.g. copying a pencil sketch) or in various ways with instruments or measurements (e.g. copying a particular angle with a protractor). Alternatively, it may imitate the sample (e.g. an action), and this too in many different respects. Since copying is a characteristic use of samples, and since objects are characterized as samples in respect of how they are used, it is tempting to conclude that the meaning of ‘sample’ varies systematically with differences in what counts as copying (MS 114 (Vol. X) Um., 66 = PG 91). Reproducibility is equally important. It is a feature of typical samples or specimens in natural science, of fair samples in statistical sampling, and of standards used in weighing and measuring.7 But what counts as reproducing samples depends on purpose and context. Moreover, the possibility of reproducing samples does not guarantee parity of esteem between the parent sample and its ‘offspring’; for example, the standard metre may have metre sticks as its ambassadors, but it is still prince. Thirdly, a sample has a normative role. It can be used as a standard of comparison (though what counts as comparison varies (BB 84ff.)). The notion of ‘standard of comparison’ must be construed liberally. The root idea is familiar: if one gives a painter a colour sample to copy in decorating a wall, one will blame his work, not the sample, if one ﬁnds that they do not match. The sample is what measures, not what is measured. Samples typically function as standards of correctness and error; we appeal to them in justifying or criticizing copies and reproductions. Wittgenstein’s realization that samples invoked in explaining what words mean can be considered to be part of grammar, that they belong to the means of representation, not (as long as they are being used as samples) to what is represented, was a crucial step in undermining the idea of a ‘connection between language and reality’. Such word–world connections were supposed to be the source and foundation of linguistic meaning. For according to this conception, 7

It is one of the features emphasized in Wittgenstein’s characterizing mathematical proofs as paradigms.

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words are either deﬁnables, which are intra-linguistically explicable, or indeﬁnables, which are directly linked to entities in the world that are their meanings. Accordingly, meaning is, as it were, injected into the network of words by means of the indeﬁnables. That idea had guided the Tractatus and had been prominent in the philosophical tradition. A corollary of its repudiation was that patterns of internal relations which had hitherto appeared to be part of the objective essences of things now became perspicuously features of our means of representation (in particular, of our use of samples). This merits closer scrutiny. Red is darker than pink; it is more like orange than it is like yellow; and nothing can be red all over and green all over simultaneously. Similarly, three metres is longer than two metres; and nothing can be both two metres long and three metres long at the same time. (Examples can be multiplied by reference to other determinates of determinables, e.g. notes of the octave or weights.) These propositions are evidently not empirical propositions. They are a priori. It is inconceivable that red should be lighter than pink or more like yellow than like orange. So such propositions are necessary truths. But on no account of analyticity are they analytic propositions. (For example, they are not derivable from explicit deﬁnitions and the laws of logic alone (Frege’s explanation of ‘analytic’), since there are no explicit deﬁnitions of colourwords.) So they seem to be to be synthetic a priori propositions describing the essential natures of things. Hence they are apparently de re necessary truths, that describe the essential natures of the relevant colours (lengths, weights, notes of the octave). Clariﬁcation of the role of samples in our means of representation enabled Wittgenstein to brush this conception aside as a confused projection of grammatical conventions on to reality. Of course, red is darker than pink. That is actually no more than a grammatical proposition, i.e. an expression of a rule for the use of words in the misleading guise of a statement about things. It is a rule to the effect that if A is red and B is pink, we can, without more ado (in particular, without looking), infer that A is darker than B. But, one is tempted to protest, is that not simply because it is part of the essence of red to be darker than pink? For even granted that the ostensive deﬁnitions of ‘red’ and ‘pink’ are rules, the rule of inference is another separate rule. Yet there is an internal relation between being red and being darker than pink. The properties and the relation are connected. It is part of the nature of red to be darker than pink. The inference rule simply reﬂects an objective reality. — That is mistaken. It is grammar that determines the nature of things (PI §§371–3). The connection between being red and being darker than pink is forged by our convention that any ordered pair of samples that can be used respectively to deﬁne ‘red’ and ‘pink’ can also be used to deﬁne the relation ‘darker than’. The red and pink patches serve us simultaneously as a sample of the relations ‘darker’ and ‘lighter’ and as samples of ‘red’ and ‘pink’ (cf. RFM 75f.) — and it is this that determines the internal relation. Similarly, red is indeed more like orange than

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like yellow. But that merely amounts to the inference licence that allows one to infer, independently of further experience, that if A is red, B orange and C yellow, then A is more like B in colour than it is like C. This inference rule does not reﬂect objective, language-independent, internal relations. On the contrary, it is itself connected, in our linguistic practices, with the use of relevant samples to deﬁne ‘red’, ‘orange’ and ‘yellow’, inasmuch as any ordered triple of such samples can also be used to deﬁne the phrase ‘more like B than C in respect of colour’. The ‘connection, a connection of the paradigms and the names, is set up in our language’ (RFM 76). Finally, of course, nothing can be both red all over and green all over simultaneously. But that is not because one colour prevents the other colour from occupying the same place (as Wittgenstein had wrongly suggested in 1929 (RLF 169)). It is rather because we call this + ‘red all over’ and that + ‘green all over’ and we do not call this + (pointing at the red sample) ‘the same colour as that + (pointing at the green sample)’. So if A is this + colour all over, it is not also that + colour all over. What appear to be necessities in the world are no more than the shadows cast by grammar.

5. Misunderstandings resolved Wittgenstein’s account of the role of samples in grammar breaks with traditional reﬂections, and its consequences for philosophical understanding are anything but trivial. But it is prone to generate objections. (i) Mere recognitional abilities are all that is required for explaining mastery of ‘indeﬁnables’. It seems that ostensive deﬁnitions are superﬂuous in the description of what it is to have mastery of a language. Consider, for example, the fact that we may use any red object to explain ‘red’ ostensively. The ability to give an ostensive explanation of ‘red’ is therefore parasitic on our recognitional ability to pick out red objects. So having that ability (and applying ‘red’ accordingly) is what understanding ‘red’ consists in.8 Therefore, the ability to explain ‘red’ either presupposes or collapses into the ability to apply ‘red’ correctly. This makes ostensive deﬁnitions of ‘red’ superﬂuous. Why should one presume that there are two distinct things involved in understanding ‘red’: namely, agreement in judgements and agreement in deﬁnitions (i.e. in choice of objects as samples for explaining ‘red’)? Correct application appears to be the sole criterion of understanding here. (ii) Samples are relevant only to the genesis of understanding. It seems that the relation of concrete samples to the applications of words is typically a case of 8

This is a generalization of the following remark: ‘The idea that someone may have a capacity for recognizing an object which he cannot further explain is in no way absurd . . . a grasp of a name might, on occasion, consist in its association with just such a capacity . . .’ (M. A. E. Dummett, ‘Frege’s Distinction between Sense and Reference’, repr. in his Truth and Other Enigmas (Duckworth, London, 1978), p. 129).

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action at a distance, and hence that samples are not part of the grammar of words. How, for example, does the standard metre, used in explaining the expression ‘one metre’, enter into typical applications of this expression? Certainly not as an ‘object of comparison’, if that describes an instrument held up against a measured object. Similarly how is a red book which one now uses to explain ‘red’ involved in subsequent applications of ‘red’, whether one’s own or the learner’s? It seems that explanation by samples is relevant only to the genesis of understanding.9 (iii) Expressions deﬁned by reference to samples are implicitly relational. It seems that the employment of samples in explaining or applying an expression makes it implicitly relational.10 If ‘red’ is ostensively explained by pointing to a red book, does this not imply that an object is red if and only if it resembles this book in colour? Hence, in describing an apple as red, one is simply saying that it resembles this book in colour, and so asserting a relation to hold between it and this sample. Similarly, if one uses a metre stick in measuring objects, the statement that a table is one metre long is simply equivalent to the assertion that it has the same length as the metre stick. (iv) The role of samples is incompatible with the principle that meaning must be independent of the facts. If explanations by sample are treated as substitutionrules, and particularly if samples are indispensable for explaining some expressions, it seems that language gives hostages to fortune.11 The destruction of a sample or its appropriate alteration would have grammatical repercussions: for example, loss of, or damage to, the standard metre would transform the system of metric linear measurement. How can the presence of concrete samples in the grammar of our language be reconciled with the principle that the meaning of a sentence must be independent of the facts?

9 See, e.g. W. V. O. Quine: ‘Many expressions, including most of our earliest, are learned ostensively; they are learned in the situation that they describe, or in the presence of the things that they describe’ (Philosophy of Logic (Prentice-Hall, Englewood Cliffs, NJ, 1970), p. 6). There is, according to Quine, nothing normative about ostensive teaching: ‘This innate qualitative spacing of stimulations was seen to have one of its human uses in the ostensive learning of words like “yellow”. . . . this is not the only way of learning words, nor the commonest; it is merely the most rudimentary’ (‘Natural Kinds’, repr. in his Ontological Relativity and Other Essays (Columbia University Press, New York, 1969), pp. 121f.). 10 See, e.g. R. Carnap: ‘ostensive deﬁnitions: here the term is deﬁned by the stipulation that the objects comprehended by the term must have a certain relation (for instance, congruence or likeness) to a certain indicated object’ (Logical Syntax of Language (Routledge and Kegan Paul, London, 1937), p. 80); and Quine: ‘One learns by ostension what presentations to call yellow: that is, one learns by hearing the word applied to samples. All he has to go on, of course, is the similarity of further cases to samples’ (‘Natural Kinds’, p. 121.) 11 This was one reason for the sempiternality of objects (the meanings of simple names) in the Tractatus. As PI §55 observes, it seems that ‘What the names in language signify must be indestructible, for it must be possible to describe the state of affairs in which everything destructible is destroyed. And this description will contain words; and what corresponds to these cannot be destroyed, for otherwise the words would have no meaning’. (See Exg. §55.)

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These objections arise from confusions that the Investigations was meant to eliminate. Before resolving them, it will be useful to introduce some further terminology to mark distinctions among the ways that samples function in grammar. (It should be stressed that this is going beyond anything Wittgenstein wrote.) (i) Canonical samples: sometimes an object used as a sample has a unique role in our practice. Such a sample is ‘canonical’. Canonical samples are prominent in systems of weights and measures: the standard metre and the standard kilogram in Paris, the Imperial Standard Bar at Greenwich, etc. We deﬁne (or rather, used to deﬁne) the unit of length one metre as the length of the standard metre, the unit of mass one kilogram as the weight of the standard kilogram, etc. Because of their limited availability, canonical samples are not typically employed in ostensive deﬁnitions or as instruments of comparison for determining the application of the deﬁned expression. Rather, they are used in giving explanations by samples picked out by a deﬁnite description or proper name; for example, ‘one metre is the length of the standard metre’. An explanation by reference to a canonical sample may well not be the only explanation the giving of which is a criterion of understanding the explanandum. One may explain the phrase ‘one metre’ by pointing to an ordinary metre stick and saying ‘That is one metre long’. None the less, the unique role of a canonical sample gives explanations by reference to it a certain primacy among admissible explanations. This reﬂects its typical function as a pattern for the production and calibration of objects used as standard samples (see below). This normative role is important whether or not there are actual appeals to the canonical sample in settling disputes, indeed whether or not most of the participants in a system of measurement are even aware of the existence or role of the canonical sample in this institution (cf. ‘The standard metre’, pp. 193). (ii) Standard samples: in order to secure general agreement in judgements in conformity with our normal requirements of precision, we must judge the applicability of certain concepts by using objects as standards of comparison. The model for this procedure is measurement of length by a ruler. We cannot judge lengths without rulers accurately enough to serve most practical and theoretical purposes; we must make use of instruments of measurement, laying a measuring rod against the object to be measured and reading the length off from the calibrating marks. Metre rules, yardsticks, tape measures, etc. have this function; so too do kilogram weights, colour-charts and tuning forks. Objects so used may be called ‘standard samples’, provided that their functioning thus is part of our practice (and not merely justiﬁed by inductive argument). Measuring and weighing play important roles in human life in all but very primitive societies. The availability of plentiful and accessible standard samples has obvious advantages. But small differences in measurement are often important, and uniformity in standards of measurement is required. This makes it urgent to have a procedure for ensuring uniformity of standard samples. One

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remedy is to adopt a canonical sample for each unit of measurement — for example, the king’s foot or the standard metre — and to calibrate standard samples by reference to it. Another is to ﬁx a recipe or authoritative procedure for calibrating standard samples by reference to natural constants. (Each of these strategies presupposes agreement on methods of matching the putative standard samples with the ‘control’, and these methods may vary according to our purposes.) (iii) Optional samples: objects play a less institutionalized and permanent, but none the less important, role in the practice of explaining a wide range of expressions. This is evident in explanations of words for simple perceptual qualities, for example, ‘red’, ‘sweet’, ‘acrid’, ‘musty’, ‘rough’, ‘hard’, ‘cool’. We explain ‘red’ by pointing at some object clearly exemplifying the colour red and using it in the context of this ostensive deﬁnition as a sample. Such a sample is not ﬁxed permanently like a canonical sample. No object serves invariably in this explanatory role, nor does every explanation of ‘red’ employ the same object. An object may serve this role even though it is not used as a standard of comparison. What is essential is its (transient) role in giving an explanation. Such samples may be called ‘optional’. Relative to particular contexts of explanation, optional samples belong pro tempore to grammar. The status of an object as an optional sample is context-relative. What is now used as a sample for explaining ‘red’, for example, may on another occasion be described as red. This may seem strange. Surely if something functions as a standard, it must enjoy a degree of permanence. We are inclined to forget that characterizing something as a sample does not turn on its intrinsic properties, but on how it is used. If we bear this in mind, the ephemeral status of optional samples is no more odd than the practice of a group of children who, wishing to play football in a ﬁeld lacking goal-posts, use four among themselves to stand as post-markers on the understanding that these will swap places with other players whenever a goal is scored. What the use of colour-words presupposes is agreement in deﬁnitions, i.e. an agreed practice in explaining them. This does not require permanently ﬁxing some objects as samples, but only a substantial agreement on whether explanations by reference to particular samples are correct. There are stable rules for the use of colour-words; but although every legitimate explanation of ‘red’ makes use of a sample, it does not follow that there must be some permanent sample of which every legitimate explanation makes use. Calling something an optional sample characterizes only its role in the practice of explaining an expression. This is independent of whether it has in addition the role characteristic of standard samples in applying the explanandum. An object, for example, a particular metre stick, may have both roles. But many optional samples are not also employed as standards of comparison — for example, samples invoked in explaining colour-words, such as ‘blue’, ‘red’ — and ‘green’. Our recognitional abilities in respect of such colours are adequate, and we normally have no need for recourse to samples in applying

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these words. However, people’s recognitional capacities with regard to shades of colour vary. One person may not need a sample to pick out a scarlet or magenta cloth, whereas another will need a sample to use as a standard of comparison ( just as all of us need a tape measure or ruler to judge precise lengths of cloth).12 Armed with these distinctions, we can outline ways of resolving the above four problems concerning Wittgenstein’s account of ostensive deﬁnition and samples. (i) It is mistaken to suppose that the assimilation of samples into the means of representation is redundant, and that recognitional capacities alone sufﬁce to explain our mastery of such terms as ‘red’ or ‘green’. It is correct that in order to make use of samples of red or green, one must possess the appropriate recognitional capacity. That is why the blind cannot acquire proper mastery of colour concepts — they cannot pick out samples, and hence cannot master their use as standards of correctness. But it is false that correct application is the only criterion of understanding a word explained by optional samples. First, our linguistic practice does treat giving an ostensive deﬁnition of ‘red’ as a criterion of knowing what ‘red’ means (PG 83); to deny this is to misdescribe the grammar of the phrase ‘to know what “red” means’. Secondly, giving an ostensive explanation by pointing to a red object is not to describe this thing as being red; it is not to apply the word ‘red’ to anything. The immediacy of many colour judgements fosters the illusion that samples have no part in the grammar of colour-words. But the use of language presupposes agreement in deﬁnitions as well as agreement in judgements (see Exg. §242). (ii) The idea that samples enter only into the genesis of understanding, and hence do not belong to grammar, is attractive primarily in the case of explaining what a word means by reference to an optional sample. But even here it fails to grasp the difference between a predication of ‘red’, for example, and a deﬁnition of the word. Hence it fails to see that ‘This colour + is red’ gives a rule for the use of the word ‘red’: namely, that anything that is this colour + may be said to be red. It might be conceded that an ostensive explanation does indeed give a rule for the use of a word, but still insist that its role is exhausted in teaching the use of the word, and that thereafter it drops out. For, as Wittgenstein himself remarked, there is no action at a distance in grammar (PG 81). This objection rests on an over-simple conception of what it is to follow a rule (i.e. an explanation of meaning) in applying a word. By implication, it recognizes as part of the grammar of a word only samples serving as standards of comparison. 12

Of course, there are contexts in which we all use standard samples of colours for specialized purposes. Colour-charts are used for the precise description or speciﬁcation of shades of colour; in duplicating the paint on a wall, we might hold a paint-card against the wall, comparing the patches of colour with the painted surface for match and mismatch, or we might use a colour-chart to label the product of a paint factory with the British Standard numbers (e.g. ‘06 C 18’).

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Only these are deemed to enter into the application of the word; other samples are held to act only at a distance. This is too restrictive a conception of the role of samples belonging to grammar. It fails to take into account their role in criteria of understanding, in establishing agreement in deﬁnitions, and in justifying the application of a word in disputed cases. It also involves an excessively narrow conception of following a rule. For it is wrong to suppose that one is following a rule only when the rule explicitly ‘enters into’ the act or activity. The chess master is following the rules of chess in the course of the game no less than the novice who consults them (see Volume 2, ‘Following rules, mastery of techniques and practices’, sect. 1). (iii) The conception that any expression explained or applied by reference to a sample must be implicitly relational springs from conﬂating explanations with applications of words. Then it may well seem that an ostensive explanation of ‘red’ is really elliptical: the full form would be to point at a red object and to say ‘This is red, and so is anything similar to this (in respect of colour)’. So describing another object as red is justiﬁed by this rule provided that that object resembles this one (in colour). This is misconceived. First, it is no explanation of what ‘red’ means to say that something can be said to be red if it resembles a red object. Secondly, an ostensive deﬁnition of ‘red’ does not describe an object as being red. A fortiori, to say of some other object that it is red cannot be to describe it as having the same colour as the sample, e.g. a ripe tomato. For the ostensive explanation did not predicate ‘red’ of the tomato; it explained that the colour of the tomato is (called) red. And to say that some other object is red is to describe it as being that + colour (pointing at the sample), not: the same colour as that + object. Similarly, a standard sample employed as an object of comparison in applying an expression is not something thereby described; for example, in measuring a table with a metre stick a person does not describe the metre stick at all. A fortiori, in justifying the assertion that the table is one metre long by measuring it with the metre stick he is not describing the table as resembling the metre stick in respect of length. To say that an object is one metre long because it coincides with the metre stick asserts no more than that it is one metre long. The ‘because’ clause simply recapitulates an explanation of what it is for something to be one metre long (namely, to be that + length). (iv) The objection that samples in grammar give hostages to fortune seems most compelling in the case of canonical samples, though it applies also to standard and optional samples. This issue will be examined in ‘The standard metre’ below. For the moment it must sufﬁce to point out that the principle that meaning must be independent of the facts does not imply that instruments of language, such as samples, must be sempiternal, and immune to the vagaries of fortune. Whether something is a sample depends on our use of it. We can cease to use something as a sample if we please, and, conversely, if something we hitherto used as a sample is damaged or destroyed, we can typically manufacture or settle on a new sample.

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A primary difﬁculty in grasping Wittgenstein’s insights is the appeal, in this context, of Platonism and idealism. It is difﬁcult to recognize that concrete objects used as samples in explaining or applying expressions belong to our method of representation (to grammar). We are tempted to think that these objects are merely incidental, that the real samples are Platonic entities (e.g. the length of the standard metre, the colour of the patch on the chart), or mental objects (e.g. the image of this colour in the mind of the perceiver). Wittgenstein warns against the temptations of Platonism: In this case, too, you cannot say: ‘A ruler does measure in spite of its corporeality; of course a ruler which only has length would be the Ideal, you might say the pure ruler.’ No, if a body has length, there can be no length without a body — and although I realize that in a certain sense only the ruler’s length measures, what I put in my pocket still remains the ruler, the body, and isn’t the length. (PR 81)

This will be further explored below (see ‘The standard metre’). The private language arguments (PI §§243–315) include a sustained attack on the idealist gambit (see Volume 3, ‘Private ostensive deﬁnition’).

6. Samples and simples Wittgenstein’s reﬂections on samples and ostensive deﬁnition emerged in part from detailed reconsideration of his earlier ideas. Consequently, it should not be surprising that the conception of samples and of their role in grammar sheds light on the conception of simple objects in the picture theory of representation of the Tractatus. It is now clear that the simple objects of the Tractatus included properties and relations (NB 61; LWL 120).13 It is equally clear that Wittgenstein did not think that it was part of the task of the Tractatus — a treatise on logic — to investigate the objects which constitute the substance of the world. That was a task for the application of logic (TLP 5.557), i.e. for the analysis of the contents of elementary propositions. This he had supposed to be irrelevant to logic, since, given the independence postulate for elementary propositions, all logical relations seemed to be determined by the truth-functional combinations of elementary propositions, and none by the contents of elementary propositions (logic, he thought, must be topic-neutral). When he took up the analysis of the contents of elementary propositions in 1929, it did not take him long to realize that the demands he had laid on objects were inconsistent, as indeed was the idea of the topic-neutrality of logic. 13

It is also evident from the examples Wittgenstein gave of objects in his numerous later discussions of the Tractatus (see Exg. §104). Of course, these examples do not fully satisfy the requirements on objects — but then nothing would, since they are not coherent.

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The moot question is what in fact fulﬁls the needs which the Tractatus objects were invented to satisfy. To the extent that these needs are genuine, Wittgenstein realized, the proper answer to this question is (at least in part) ‘samples’. In an early reconsideration of the matter, he called the four primary colours ‘objects’ and characterized them as elements of representation (WWK 43). Hence the question ‘Are objects thing-like or property-like?’ is meaningless, inasmuch as they belong to the means of representation and not to what is represented. What he had meant by ‘objects’ was whatever we can speak of without fear of non-existence (PR 72), and he cited as possible instances ‘the four basic colours, space, time, and other data of the same sort’ (PR 169). Similarly, ‘If you call the colour green an object, you must be saying that it is an object that occurs in the symbolism. Otherwise the sense of the symbolism, and thus its very existence as a symbolism, would not be guaranteed’ (PG 209; cf. BB 31; PI §46). To be sure, it took him some time fully to clarify the matter. Comparing the objects of the Tractatus with samples is illuminating, for it reveals the extent to which the former are in effect distortions of the latter. (i) Objects are simple (TLP 2.02). Samples too may be simple relative to a particular language-game (PI §48). (ii) Objects are necessary existents, their existence being required by logic, as a condition of the possibility of language (TLP 2.0211, 6.124). This idea is encapsulated in the supposition that to imagine the non-existent is to imagine non-existent combinations of existing elements (cf. Descartes, Meditations I). We are inclined to think that ‘the elements, individuals, must exist. If redness, roundness and sweetness did not exist, we could not imagine them’ (BB 31). But ‘What looks as if it had to exist, is part of the language. It is a paradigm in our language-game; something with which comparison is made’ (PI §50). It appears as if redness must exist in order for us even to say that something is not red — ‘what the names in language signify must be indestructible; for it must be possible to describe the state of affairs in which everything destructible is destroyed’ (PI §55). But this was an illusion. To be sure, ‘something corresponding to a name, . . . without which it would have no meaning is a paradigm that is used in connection with the name in the language-game’ (ibid.). But, of course, the samples that deﬁne such words do not have to exist. If red samples did not exist, we would not have our concept of red. If we lacked canonical samples of lengths and weights, we would not have the system of measurement that we now have. Samples are not necessary existents, but instruments in the language-games we play. If we lacked certain samples or lost the ability to use them correctly, we would have lost certain instruments of language and would not have the same uses for words hitherto explained by reference to them. Language, far from resting on metaphysical foundations, is autonomous and self-contained. (iii) A state of affairs is a combination of objects (TLP 2.01). The objects which are constitutive of a state of affairs hang together like the links of a

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chain; no metaphysical glue in the form of a relation is necessary for the combination of objects (TLP 2.03). It is easy to see that the plausibility of this is related to the confusion of samples that belong to the means of representation with objects represented. One can readily think of the fact that a given circle is red as a combination of a circle and redness or of circularity and redness (PG 200). The ‘object’ red needs nothing extra to ‘combine’ with the ‘object’ circularity to constitute the fact that this circle is red. Although this is nothing but confusion and mystiﬁcation (PG 199ff.), the confusion is illuminated by reﬂection on samples and ostensive deﬁnition. (iv) The combinatorial possibilities of objects are metaphysically predetermined, and every possible combination is necessarily possible (TLP 2.012– 2.0121). These metaphysical necessities are mirrored in the logico-syntactical rules of language. Later, Wittgenstein criticized these alleged metaphysical necessities as mere projections of grammar onto reality. Colours can ‘combine’ with shapes, but not with sounds. But this is no law of ultra-physics, merely a reﬂection of the fact that we assign a sense to ‘This circle is red’ and do not assign any sense to ‘This note is red’. To know an object is to know all its possible occurrences in states of affairs (TLP 2.0123). This amounts to no more than the elementary truth that to know the meaning of a word deﬁned by reference to a sample is to know the rules for its use, its combinatorial possibilities in grammar, and the conditions of its application by reference to the standard provided by the sample (as used by us). (v) Objects stand in internal relations (TLP 4.123), which ‘cannot be said’ in language, but only shown (TLP 4.122, 4.124). The only analogical example Wittgenstein gave was of the internal relation between light blue and dark blue (TLP 4.123). The confusion was salutary, for it exempliﬁes how readily we confuse a form of representation with the representation of a form. First, the apparent metaphysical necessity expressed by the claim that dark blue is darker than light blue, is, as we have seen, fully explained by reference to the use of appropriate pairs of samples (RFM 75). Secondly, sentences such as ‘White is lighter than black’ are expressions of rules for the use of the constituent terms. They are ‘grammatical propositions’, not descriptions of de re necessities. ‘White is lighter than black’ looks like ‘This object is lighter than that one’ (since the object that is now lighter may darken later). But that is deceptive. The grammatical proposition ‘White is lighter than black’ is a misleading form of words that says no more than that it makes sense to speak of two objects, the lighter one white, the other black, but not vice versa (RFM 48). (vi) ‘If two objects have the same logical form, the only distinction between them, apart from their external properties, is that they are different’ (TLP 2.0233). So, in so far as colours, or minimally discriminable shades of colour, were thought to be objects (cf. RLF), it seemed clear that they all have the same logical form. External properties apart, the only difference between them is that they are different (colours or shades of a colour). But this was a misguided projection of the fact that the only relevant difference between

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samples of two determinates of the same determinable is that they are samples of two different determinate-names (chromatic colour-names). For they severally serve to deﬁne words that belong to the same grammatical category. Of course, the question ‘What is the difference between red and blue?’ is meaningless, unless we take the object that has the colour to be a distinguishing mark of the colour (PG 208) — which is itself absurd. (vii) Objects can only be named, not described (TLP 3.221). When we explain what ‘red’ means by giving an ostensive deﬁnition, it indeed appears that the ‘object’ in question (the colour) is named, and that nothing further can be said of it; it cannot be described, except by speciﬁcation of its external properties, which are inessential features of the ‘object’. But all that this amounts to is the lexical indeﬁnability of a word like ‘red’ (PG 208). The red sample is not an object which lies beyond the descriptive powers of language, but is itself an instrument of language (cf. Exg. §§48f.). (viii) A name means an object, the object is its meaning (TLP 3.203). Names connect language with reality. This picture is at the root of the confusions embodied in the Tractatus (cf. WWK 209f.). What is there construed as a connection between language and reality is a correlation in grammar between name and sample. The sample is not the meaning of the name, but an instrument in the explanation of its meaning. The meaning of an expression is its use. The objects of the Tractatus, one might say, were samples ‘seen through a glass darkly’.

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

VI

Indexicals At various places Wittgenstein gives some attention to indexical expressions. He normally concentrates upon ‘this’, but also touches on ‘here’, ‘there’, ‘now’, ‘then’, ‘yesterday’, ‘a year ago’, etc. Among the ﬁrst-person pronouns, ‘I’ is extensively discussed, the distorted picture of its use being the source of deep illusion. The only pertinent point here is that ‘I’ is not the name of a person. The radical claim that ‘I’ is not a referring expression at all is examined in Volume 3, in an essay entitled ‘I and myself ’. The term ‘indexical’, coined by Peirce, serves to emphasize the fact that in order to understand what is said by uttering some sentence containing words like ‘I’, ‘this’, ‘here’, ‘now’, etc., one must know such things as who uttered it, what he was pointing to, when and where he was when he spoke. Others use different terminology, e.g. ‘egocentric particulars’ and ‘tokenreﬂexive words’. It should be emphasized that the uses of these pronouns or noun (or noun-phrase) determiners and place- or time-relaters is manifold. It would be preferable to speak of their indexical use rather than to speak of them as indexicals. The particular use of ‘this’ and ‘that’, ‘these’ and ‘those’, which has attracted philosophical attention is the deictic or ostensive use, in which the word is used as a demonstrative pronoun and is accompanied by a gesture of pointing. But other uses must be borne in mind. Discourse reference, whether anaphoric or cataphoric, is common (‘That (this) is what I meant (mean)’). ‘Here’ and ‘there’ are similarly used as pro-forms for place adjuncts (‘Look in the top drawer, you’ll ﬁnd it there’). The use of these expressions as noun or noun-phrase determiners is common, as in ‘this horse’ or ‘that old car’. Such determiners are often used to signify co-referentiality of two noun phrases, whether they have identical heads or not (e.g. ‘He was given a bay mare for his ﬁfteenth birthday. What a lot of fun he had with that mare.’ Or ‘The boy with black hair is in our team. That lad is a good player’). ‘This’ and ‘that’ can function as intensiﬁers pre-modifying an adjective ‘. . . this good’, ‘. . . that empty’, and may have anaphoric reference (‘There are three hundred people in the Hall. I didn’t expect it to be that full’). ‘This’, ‘these’, ‘that’, ‘those’, together with such adjectives as ‘very’, ‘same’, ‘identical’ can be used to indicate identity of type of object rather than co-referentiality (‘He bought a Jaguar XJ6. I bought that same car three years ago’). ‘Like’ together with ‘that’ is even clearer: ‘He reads the News. I wouldn’t read a paper like that.’ ‘That which’ often functions

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as a quantiﬁer, as in ‘That which glitters is not always gold’. Examples could be multiplied, but these sufﬁce to discourage hasty generalization. Though critical in intent, Wittgenstein’s discussion of indexicals does not take the form of confronting philosophers’ generalizations with a full list of indexical expressions and a complete tabulation of their multifarious uses. Hence no such detailed survey is necessary to follow his argument. He does not even cite mistaken theses about indexicals and subject them to careful examination. Although Russell is mentioned, criticism is not so much targeted on him as directed at a very general position exempliﬁed in his writings. Wittgenstein’s central criticism is that even if we allow the syntactical concept of a name as generous a scope as is compatible with its retaining signiﬁcant content, ‘this’, ‘that’, ‘here’, ‘there’, ‘today’, ‘now’, ‘then’, etc. are not names. His argument contrasts the uses of names with the uses of indexicals, and also the explanation of names with the explanation of indexicals. Frege had little to say about indexical expressions or the indexical use of these expressions. He merely mentions them in noting that a contextdependent sentence does not express a complete thought (BLA i pp. xvi f.; Thoughts’ (CP 65f.)). The use of such a sentence on appropriately different occasions expresses different thoughts, and what thought is expressed is a function not only of the sentence uttered but also of the context (including the speaker) of its use. Thus, the time of an utterance is part of the expression of the thought expressed by a sentence in which words such as ‘today’ or ‘yesterday’ occur, and similarly the place (‘here’), the ostension (‘there +’) and the speaker (‘I’). Pronominal indexicals would seem to count, on Frege’s criteria, as degenerate proper names. They satisfy his superﬁcial syntactical criteria for being a proper name. Their role (perhaps with the exception of the ﬁrst-person pronoun) is indeed that of a Fregean proper name, i.e. to single out a subject of discourse, a referent which is an ‘object’.1 They are degenerate in that they cannot fulﬁl this role without ‘aid from outside’, as it were. Their sense is incomplete, though incomplete in a rule-governed way. Each singles out a referent only together with a systematic contextual supplementation. (If, like Frege, we claim that the place, time, speaker, object pointed at, etc. are part of the expression of the thought, then the indexical together with its counterpart is not, in any ordinary sense, a referring expression. ‘There +’ picks out a place, but ‘There +’ together with the place does not pick out a place.) It is noteworthy that Frege does not have any notion of meaning which would be suited to a discussion of these uses of expressions. For one clearly wants to say that ‘this’, ‘today’, ‘here’, etc. have constant meanings, even though 1

According to Wittgenstein, that is precisely what the ﬁrst-person pronoun does not typically do. When I groan ‘I am in pain’, when I announce ‘I am going’, or when I volunteer ‘I’ll do it’, I am not singling myself out from among others with whom I might be confused, I am drawing attention to myself. For examination of his account of the ﬁrst-person pronoun, see Volume 3, ‘I and my self’.

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their senses as conceived by Frege are incomplete, and when completed vary from occasion to occasion. This is not a wholly peripheral matter. Contextdependence is a pervasive feature of language. To understand such expressions in language is to know how to use them, to grasp rules that govern their use, inter alia in making references. On Frege’s account they do not have a sense (or, at any rate, a complete sense). But they are not meaningless. Their use can be explained and understood. Unlike Frege, Russell had a lifelong preoccupation with indexicals (‘egocentric particulars’).2 This was determined by his denotational conception of meaning and his quest for epistemologically guaranteed foundations for language (see ‘Logically proper names’, sects 1 and 3). Genuine names, i.e. names from a logical point of view, according to Russell, are characterized by the following features: (i) they have meaning in isolation (are not incomplete symbols); (ii) they stand for particulars; (iii) the particular for which a name stands is its meaning; (iv) its meaning is a simple object logically independent of every other existent; (v) proper names are simple symbols; (vi) they cannot occur in sentences of the form ‘ξ exists’ (see ‘Logically proper names’, sect. 1). Indexicals seemed to ﬁt this bill. ‘This’ appears to have, in its meaningful indexical use, a guaranteed reference (if it fails to refer, nothing with a meaning was uttered). It ‘stands for’ a particular (in its most common use), it is arguably a ‘simple symbol’, and ‘This exists’ makes dubious sense, at any rate in standard contexts. ‘This’ carries no descriptive load at all, and by its use one (normally) means such-and-such an object. Russell’s conception of logically proper names (unlike that of the Tractatus) demanded an epistemological guarantee that such a name does refer. He wished to ensure certainty that a name has meaning. This is secured by the principle that only an object of acquaintance can be named. Acquaintance with a particular is both necessary and sufﬁcient for understanding a name (PLAt 181). Russell concluded that only actual objects of sense can be named. That makes it very difﬁcult to get any instance of a name at all in the proper strict logical sense of the word. The only words one does use as names in the logical sense are words like ‘this’ or ‘that’. One can use ‘this’ as a name to stand for a particular with which one is acquainted at the moment. We say ‘This is white’. If you agree that ‘This is white’, meaning the ‘this’ that you see, you are using ‘this’ as a proper name. But if you try to apprehend the proposition that I am expressing when I say ‘This is white’, you cannot do it. If you mean this piece of chalk as a physical object, then you are not using a proper name. It is only when you use ‘this’ quite strictly, to stand for an actual object of sense, that it is really a proper name. (PLAt 179)

Russell thus concluded that the only words used as proper names were the indexical pronouns ‘this’ and ‘that’. From a Cartesian point of view, only one’s use of ‘this’ is proof against a malin génie. These names were meaningful, but 2

For this terminology and Russell’s ﬁnal, bizarre view, see IMT, ch. 7.

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no one other than their user could know what they meant. Their meanings were conceived as essentially private. This did not disturb Russell at all: It would be absolutely fatal if people meant the same things by their words. It would make all intercourse impossible, and language the most hopeless and useless thing imaginable, because the meaning you attach to your words must depend on the nature of the objects you are acquainted with, and since different people are acquainted with different objects, they would not be able to talk to each other unless they attached quite different meanings to their words. (PLAt 174)

Not only was the meaning of such a word incommunicable, but it was also conceived to be radically ambiguous, for ‘it seldom means the same things two moments running’. Although Russell ultimately repudiated these doctrines and replaced them by others in his later works Inquiry into Meaning and Truth and Human Knowledge, its Scope and Limits, there is no need to pursue his confusions further, since his later views post-date the criticisms of the Investigations. Indexicals are not discussed in the Tractatus. The only pertinent remark in the Notebooks is the following opaque observation: ‘What seems to be given us a priori is the concept: This — identical with the concept of the object’ (NB 61). Since the concept of an object is a formal concept (hence a variable in a logically perspicuous notation), ‘this’ is evidently not taken to be a logically proper name, but an expression of the general form of all names. It may well have seemed to Wittgenstein that the simplicity of objects is reﬂected in the expression ‘this’ that is the general form of logically proper names that have objects as their meanings. How he conceived of the use of the demonstrative when coupled with a deictic gesture, as in ‘This + is A’ is obscure. A later remark (PR §6) suggests that he thought of such a sentence as a truth-value bearing description that serves as an elucidation of a simple and indeﬁnable name (TLP 3.263). In his post-1929 writings Wittgenstein describes our use of indexical expressions, compares and contrasts their use with that of names, and reveals what similarities blind one to the deep differences between these kinds of expression. The issue is of general signiﬁcance because it is a constant element in the illusory procedure of private ostensive deﬁnition, and hence in the private language arguments, in solipsism and idealism, and in the conception of perceptual (secondary) qualities as essentially subjective. There are superﬁcial similarities between proper names (and even other names, such as names of colours) and ‘this’. Both types of expression occur in an ostensive deﬁnition, where we point to an object. One can answer the question ‘What colour is this?’ by saying ‘Yellow’; and answer ‘What is yellow?’ by pointing and saying ‘This’ (PI §38). Furthermore, a name and ‘this’ can often (but not always) occupy the same position in a sentence, e.g. ‘Jack is short’ and ‘This is short’ (BB 109). This much is correct. There are also illusory similarities. If one thinks that a name must have a bearer, that it must be certain

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that it has a bearer, that the bearer is what the name means, one will also be tempted to think, as Russell did, that ‘this’ is a name, since it seems like a dart that cannot miss the bull’s-eye. Finally, since what the speaker means by ‘this’ is its referent, it is tempting to think that the meaning of ‘this’ is its referent. Yet all this is misleading: ‘. . . nothing is more unlike than the use of the words “this” and the use of a proper name — I mean the games played with these words, not the phrases in which they are used’ (BB 109). It is characteristic of names, according to Wittgenstein, that they can be explained ostensively — a procedure in which a sentence of the form ‘This is A’ is used. But it makes no sense to explain the use of ‘this’ by an ostensive deﬁnition of the form ‘This is this’, nor that of ‘here’ by ‘This is here’. Moreover, ‘this’, in its demonstrative use, is accompanied by an ostensive gesture, but the use of names is not. ‘This’ without the ostensive indication (or some alternative indication) is useless; names are not. Trivially, ‘this’ is demonstratively used only in the presence of the object pointed at, but names are frequently used in the absence of their bearers. The roles of the two types of expressions are fundamentally different. ‘This’ is no more the name of an object than ‘now’ is the name of a time, ‘here’ of a place, or ‘I’ of a person. An indexical expression does not differ from the corresponding name as a hammer from a mallet, but as a hammer from a nail (BB 108). ‘Here’ and ‘now’, in their indexical use, are akin to the point of origin of a system of co-ordinates. They ﬁx an ‘index’ by reference to which a host of related terms are employed, relative to that index, to pick out places and times, e.g. ‘over there’, ‘n miles away’, ‘yesterday’, ‘tomorrow’, ‘last year’, etc. They are not names of times or places, they do not designate a time or place in contrast to other times or locations, but are, rather, geometrical concepts, perhaps akin to the centre of one’s visual ﬁeld (BT 523f.). ‘Today’ is not a date, and one cannot informatively write at the head of a letter ‘Here, now’, although if one writes the place-name and date at the head of the letter, one can begin the ﬁrst sentence, ‘Here, now, it is sunny and peaceful’. To master the system of indexicals is to grasp the determination of their ‘point of origin’ on any occasion of their (indexical) use, and the systematic relations that obtain between them. Wittgenstein touches by implication on the defects of the Fregean conception (BT 523–7; B i §§705–7). It looks as if the meanings of indexicals are not determined in advance of their use (since on Frege’s view they do not have a sense, or a complete sense, independently of their context; and together with such varying supplementation, their sense varies from occasion to occasion). But this is mistaken. (i) ‘Today’ does not mean something different today from what it meant yesterday; ‘here’ does not have a different meaning here from what it means over there (B i §§705, 707). This is not a case of ambiguity, as in ‘Mr White turned white’. (ii) The meanings of indexicals are laid down in advance. One teaches and explains the use of one symbol, e.g. ‘here’, even though what one says by a

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sentence containing an indexical use of ‘here’ will vary according to place of utterance. (iii) The rules explaining the use of the various indexicals give their meanings. One understands the use of these expressions if one grasps these rules and the systematic truth links between the various indexicals (temporal, spatial, personal pronominal, etc.). (iv) Hence one must distinguish knowing how to use ‘this’, and knowing what ‘this +’ is. So one must distinguish grasping the general principle governing the use of ‘this’ and grasping what is meant by a particular utterance ‘This + is F’. The fact that ‘This +’ (pointing to A) and ‘This +’ (pointing to B) can typically be replaced by ‘A’ and ‘B’ (respectively) does not show that the word ‘This’ means sometimes ‘A’, sometimes ‘B’. One can explain the general rules for the indexical use of these expressions, and one can likewise explain the meaning of an utterance which contains an indexical and hence is context-dependent. But one must not conceive the latter explanation as an explanation of the meaning of the indexical on that occasion of its use. Indexicals are not proper names, nor are they ambiguous. The relation between an indexical and what, on a particular occasion, it is used to pick out is not a paradigm of ‘the name-relation’.

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

VII

Logically proper names 1. Russell The notion of the logically proper name, by contrast with the mere grammatical name (and personal ( proper) name), played a central role in logical atomism. In ‘The Philosophy of Logical Atomism’, Russell introduced logically proper names in speaking of ‘a name . . . in the proper strict logical sense of the word’ (PLAt 179). Wittgenstein, in the Tractatus, characterized the ‘simple signs’ of which propositions are composed as ‘names’ simpliciter (TLP 3.2–3.202). Like Russellian names, these too, by contrast with the humdrum expressions that grammar characterizes as names, were conceived to be the real, genuine names. They were said to be ‘the elements of the propositional sign’ that correspond to the objects of the thought (i.e. the simple objects which the thought is about). Both philosophers agreed that ordinary names did not really fulﬁl the task which, it seemed to them, real names have to fulﬁl if atomic or elementary propositions, and so linguistic representation in general (Wittgenstein) as well as empirical knowledge (Russell), is to be possible. Despite signiﬁcant differences between the two philosophers, the correlation of logically proper names with simple objects was the pillar on which logical atomism was supported. The concept of a logically proper name in Russell’s philosophy in the second decade of the twentieth century belongs to the puriﬁed denotational conception of linguistic meaning that was made possible by his repudiation of the concept of denoting. The Theory of Descriptions removed the necessity of distinguishing meaning from denoting; hence it licensed treating all expressions that survived analysis as names whose meanings consisted simply in the objects named. As Russell’s ideas evolved, the category of logically proper names was gradually slimmed down from the wide range of humdrum names, such as ‘Socrates’ (PM 66), to the vanishing point of ‘this’ and ‘that’ (PLAt 179), which although ambiguous, are the only proper names. His salient claims regarding what counts, from a logical point of view, as a proper name were as follows. Proper names have meaning in isolation ( PM 66). In this respect, they contrast with incomplete symbols, in particular with deﬁnite descriptions and classnames, for these have no meaning until they are supplied with appropriate contexts. Three points are noteworthy. First, Russell assimilated this contention to the claim that incomplete symbols can be deﬁned only in use, not in isolation from a context (ibid.). This wrongly suggests that the contrast between

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proper names (which, when he wrote Principia, included ordinary proper names such as ‘Socrates’) and incomplete symbols (such as ‘The golden mountain’) coincides with the contrast between what can be explicitly deﬁned and what can be deﬁned only in context. This cannot be correct, however, because, according to Russell, genuine names are indeﬁnable (i.e. unanalysable), and also because incomplete symbols may well have an explicit deﬁnition (e.g. class-names can be deﬁned by the schema: α = { x | Φ x }). The intended contrast is between symbols that can be introduced by deﬁnitions, whether contextual or explicit, and those that cannot be so introduced. Such symbols (the indeﬁnables) can be understood only by acquaintance with what they stand for, and this gives them meaning in isolation from any context. Secondly, as his ideas developed, this evolved into a reﬂection of a metaphysical doctrine: namely, that every particular ‘stands entirely alone and is completely selfsubsistent’ (PLAt 179). Since the meaning of a name is what it stands for, the independence of particulars guarantees that a name has a meaning that is logically independent of any facts at all, a fortiori independent of how it is used in the context of sentences. Thirdly, Russell’s contrast between incomplete symbols and symbols with meaning in isolation from any context (proper names) has nothing to do with the valency of an expression. For simple (unanalysable) predicates, which may be monadic, dyadic, etc., likewise have a meaning in isolation (PLAt 173f.). Consequently, simple names for particulars are not distinguished from other simple symbols by having meaning in isolation. The meaning of a genuine, proper, name is the object named, its bearer. A proper name ‘directly represents some object’ (PM 66). As noted, this originally incorporated ‘proper names’ as construed by grammarians, but, as Russell’s logical atomism evolved, the class of objects that proper names can stand for shrank dramatically. Ultimately, a proper name was held to be a word ‘whose meaning is a particular’ (PLAt 178), and a particular was conceived to be a term in an atomic fact. To understand a logically proper name is to be acquainted with its bearer. A logically proper name can be used by a speaker only in application to a particular with which he is acquainted, since acquaintance with the particular named is just what his grasp of the meaning of the name consists in (PLAt 179). This is a restriction of a more general claim: understanding of any simple symbol depends on direct acquaintance with the object which is its meaning (PLAt 173f.). The word ‘red’ can be understood only by acquaintance with the colour red through seeing red objects. So too, terms of logic, such as ‘particular’, ‘relation’, ‘universal’, can be understood only by reference to ‘logical experience’, that is, by ‘acquaintance with logical objects’ (TK 97–101). Acquaintance with the object correlated with a simple symbol does not require knowledge of any of its properties, even if these properties are essential. Acquaintance with two shades of colour, for example, in no way necessitates even the knowledge that they are different (OK 145). It follows from the independence of acquaintance from ‘knowledge about’ that there can be no degrees of acquaintance

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with the object named by a simple sign, and therefore no degrees of understanding of a logically proper name (OK 144f.). The insertion of a logically proper name into the argument-place of ‘ξ exists’ yields a meaningless sentence. By contrast, the insertion there of an incomplete symbol (an ordinary proper name such as ‘Homer’ or ‘Romulus’, a deﬁnite description, or a class-name) is meaningful (TK 138; PLAt 212–21; IMP 178). A logically proper name, being an expression the meaning of which is the object it stands for, cannot have a meaning and yet not stand for anything. So if ‘N’ is a logically proper name, then ‘N does not exist’ is either false or meaningless. Russell treated existence-attributions as ascriptions of a property (namely, the property of being satisﬁed) to a propositional function. Since a logically proper name, unlike a deﬁnite description, cannot be expanded into a propositional function, it cannot meaningfully be said of the object for which the name stands either that it exists or that it does not exist. Logically proper names are names of objects whose existence is indubitable. Although one cannot say of the bearer of a proper name that it exists or does not exist, its existence cannot be doubted by the person who uses the proper name of which it is the meaning. For a name ‘can only be applied to a particular with which the speaker is acquainted’ (PLAt 178). Russell limited particulars to present sense-data. It is only when a term is used ‘to stand for an actual object of sense . . . that it is really a proper name’ (PLAt 179). Particulars are both evanescent and private. What restricts particulars to sense-data is Cartesian doubt. As Russell saw things when he wrote ‘The Philosophy of Logical Atomism’, the only particulars are sense-data. They are immune to existential doubts. So one can be absolutely certain that the name one uses to speak of such a particular has a meaning. A noteworthy feature of this doctrine is the further penetration of epistemology into Russell’s logic. The determination of the logical form of a sentence in effect rests on the outcome of an epistemological investigation. He had already argued long before that a sentence about another person’s mental state cannot be of subject/predicate form, since ‘there seems no reason to believe that we are ever acquainted with other people’s minds, seeing that these are not directly perceived’.1 The relation of a logically proper name to the particular named is external. Words are objects (or classes of objects). This makes relations between logically proper names and particulars genuine relations between objects (or between classes of objects and objects). Given Russell’s Platonist conception of universals, relations between any simple symbols and what they stand for are real relations between objects. He characterized such relations as relations of meaning. He treated any such relation as the prototype for the relations between all simple symbols and what they stand for, e.g. the relation between ‘white’ and the 1

‘On Denoting’, repr. in The Collected Papers of Bertrand Russell, vol. 4 (Routledge, London, 1994), p. 415.

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property of being white. Indeed, it was only the Theory of Types that prevented his saying that there is a unique name-relation in which every simple symbol stands to the entity that corresponds to it. The Theory of Types forced him to admit that the relation of meaning is systematically ambiguous: i.e. that strictly speaking there are as many different relations of meaning as there are types of things (PLAt 233). The name-relation, since it is a relation between self-subsistent objects, is contingent and external. That a certain name (e.g. ‘This’) means a certain particular S is not a necessary truth, and cannot be established a priori. Instead, the truth of this claim rests on the existence of a correlation between the name and its meaning. Russell’s doctrine of acquaintance restricts particulars to mental entities (sense-data). The name-relation, therefore, is established by the speaker’s momentarily correlating a logically proper name with an object of acquaintance. This was presumably conceived to be effected by a psychological act. Logically proper names, as a species of simple signs, resist analysis. They have a function in a ‘logically perfect language’ (PLAt 176), and so stand in contrast to incomplete symbols. The latter disappear altogether on analysis. The model for this is deﬁnite descriptions as treated by the Theory of Descriptions. The categories of simple symbols (or proper names ‘in a generalized sense’) and incomplete symbols are jointly exhaustive and mutually exclusive (at least until Russell, under Wittgenstein’s inﬂuence, distinguished logical operators as a further kind of symbol). Every expression either directly represents some object, or else any sentence in which it occurs must be capable of being so analysed that it disappear (PM 66). Simple symbols are explained by descriptive sentences in which they occur. Simple symbols cannot be analysed, and hence cannot be deﬁned by analysis. Such ‘primitive ideas’ can be explained only ‘by means of descriptions intended to point out . . . what is meant’ (PM *1). Russell conceives of such explanations as propositions incorporating the simple symbol, which are intended to bring it about that a person gathers which object of acquaintance it is meant to designate. What is symbolized by a logically proper name can be symbolized only by a logically proper name. This follows from Russell’s distinction between simple and complex objects: ‘those objects which it is impossible to symbolize otherwise than by simple symbols may be called “simple”, while those which can be symbolized by a combination of symbols may be called “complex”’ (PLAt 173). Since deﬁnite descriptions are not simple symbols, it appears to follow that what can be named cannot be described, and that what can be described cannot be referred to by a logically proper name. Although it might provide for the mutual exclusion of knowledge by acquaintance and knowledge by description, this consequence seems wrong. Instead of christening a present sense-datum ‘S’, I could refer to it as ‘the sense-datum I am now having’; in doing this, I would be describing what can be named and introducing an item with which I have acquaintance by means of a deﬁnite description. In fact, Russell does not intend this dictum to be so understood. In stating that

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simple objects can be symbolized only by simple symbols, he means ‘symbolized’ to be synonymous with ‘named’. He considers deﬁning ‘red’ as ‘the colour with the greatest wavelength’. This, however, is not a deﬁnition of ‘red’, he averred, but rather a true description of the colour red. The point is that ‘red’ cannot be deﬁned or analysed, though it can be described (PLAt 173f.). This presupposes that ‘the colour with the greatest wavelength’ does not symbolize red, though it describes red. Logically proper names are distinct from ordinary proper names. No ordinary proper name of a person, place or thing is logically a proper name; every one of them is an incomplete symbol (PLAt 178; PP 54f.). Russell treats them as disguised deﬁnite descriptions, holding that each of them is an abbreviation for some deﬁnite description. This, however, is not a necessary concomitant of the claim that ordinary names are incomplete symbols, for they might be incomplete symbols of a new kind (sui generis). (Both class-names and sentences expressing propositions are actually treated as incomplete symbols distinct in kind from deﬁnite descriptions (PM 44, 187.) Demonstratives (‘this’ and ‘that’) when used to refer to actual objects of sense are logically proper names. Indeed, they were the only examples of logically proper names that Russell could ﬁnd.2 (He did not consider such spatial or temporal indexicals as ‘now’, ‘then’, ‘here’, ‘there’.) Of course, demonstratives are not always, or even typically, used as logically proper names. ‘It is only when you use “this” quite strictly to stand for an actual object of sense, that it is really a proper name’ (PLAt 179). (Russell later retreated from this view, distinguishing all ‘egocentric particulars’ from names.)

2. The Tractatus The early Wittgenstein’s philosophical reﬂections, like Russell’s, were conducted within the force-ﬁeld of presuppositions characteristic of the Augustinian conception of language. But Wittgenstein’s notion of names and their role, unlike Russell’s, was purely logical. So too, his notion of the simple objects that are the meanings of simple names, unlike Russell’s, was purely metaphysical. Both philosophers were concerned with disclosing the foundations of language. Both were committed to ﬁnding a guarantee against reference-failure and consequent truth-value gaps. But Russell sought an epistemic guarantee in indubitabilia resistant to the acids of Cartesian doubt, whereas Wittgenstein sought a metaphysical guarantee. Wittgenstein, unlike Russell, was also concerned to guarantee determinacy of sense and the exclusion of all possibility of vagueness. This too seemed to be ensured if the meanings of simple names are simple objects. For, on his account, every elementary proposition, being composed 2

Earlier he had thought the personal pronoun ‘I’ was a logically proper name (PP 27f.; but cf. OK 73f.).

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of simple names alone, divides reality sharply into two; i.e. it describes a state of affairs that either obtains or does not obtain. The objects of the Tractatus are necessary existents, not indubitable existents. Hence they are not sensedata, although it is probable that Wittgenstein thought of them as objects of acquaintance. Far from being evanescent, they are indestructible and sempiternal. They are the substance of the world (TLP 2.021), and by their combinatorial possibilities they determine the range of all possible worlds. It is instructive to compare these different conceptions that constitute two different strands of logical atomism. (i) According to the early Wittgenstein, by contrast with Russell, names do not have a meaning in isolation. ‘Only in the context of a proposition does a name have meaning’ (TLP 3.3; cf. 2.0122). Hence names cannot be contrasted in this respect with deﬁnite descriptions or, more generally, with incomplete symbols (including grammatically proper names). Wittgenstein’s context principle was motivated at least in part by picture-theoretic considerations (cf. ‘Contextual dicta and contextual principles’, sect. 3). For it is only in the context of a proposition (which is a representing fact — a sentence in its projective relation to the world) that a name represents an object. This construal of the contextual dictum was correlated with a rejection of part of Russell’s metaphysics. Russell held that every particular ‘stands entirely alone and is completely self-subsistent’ (PLAt 179) — a curious contention, since he deﬁned particulars as terms of relations in atomic facts. He explained that by this he meant that ‘each particular that there is in the world does not in any way logically depend upon any other particular. Each one might happen to be the whole universe; it is merely an empirical fact that this is not the case’ (ibid.). Furthermore, since particulars are not necessary existents, no particular belongs to every possible world. Wittgenstein rejected both contentions. First, ‘Things are independent in so far as they can occur in all possible situations, but this form of independence is a form of connection with states of affairs, a form of dependence’ (TLP 2.0122). Things (objects) are essentially constituents of facts, and their forms are the grounds of all possibilities. This form of dependence is precisely mirrored by logical syntax. Hence Wittgenstein immediately added ‘(It is impossible for words to appear in two different roles: by themselves, and in propositions)’. Secondly, objects are the substance of the world. So they are common to all possible worlds. Indeed, their combinatorial possibilities determine the range of all possible worlds. They are ‘what is unalterable and subsistent; their conﬁguration is what is changing and unstable’ (TLP 2.021; cf. 2.027–2.0272). All change is to be accounted for in terms of rearrangement of objects, and all destruction in terms of decomposition of complexes. But the simples themselves are indestructible, beyond existence and inexistence. (ii) ‘A name means an object. The object is its meaning’ (TLP 3.203). Wittgenstein accepted the obvious corollary that any sentence with names ﬂanking the identity-sign on both sides is logically trivial. Indeed, this was an

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essential part of his proof that the identity-sign can be excluded from a proper conceptual notation (TLP 5.533). (iii) What it is to know what a name means or to understand the meaning of a name is of psychological concern alone (CL 68). Therefore it was not discussed, but tacitly presupposed, in the Tractatus. However, it seems that Wittgenstein subscribed to a variant of one of Russell’s theses: namely, that understanding a name is independent of knowledge of any true empirical statements about the object named. To know an object, one need not know its external properties, although one must know all its internal ones (TLP 2.01231). For one must know its combinatorial possibilities — ‘all its possible occurrences in states of affairs. . . . For a new possibility cannot be discovered later’ (TLP 2.0123). (iv) Wittgenstein agreed with Russell that the insertion of a name into the argument-place of the expression ‘ξ exists’ yields nonsense. One route to this conclusion (there are others) is via the requirement that every sentence with sense be bipolar. This eliminated the possibility of sentences expressing necessary truths except where they can be exhibited as being constructed by logical operations on constituent sentences that are bipolar. Every so-called necessary truth is either a tautology or a nonsensical pseudo-proposition; i.e. is either senseless (sinnlos) or nonsense (unsinnig). Given Wittgenstein’s conception of objects as necessary existents common to every possible world, this precluded the possibility that a signiﬁcant sentence can state the existence of an object. For the sentence ‘A exists’, where ‘A’ is a name, would not be bipolar. Since it cannot be exhibited as a tautology, it must be nonsense (unsinnig). (v) A noteworthy contrast, as already remarked, between Wittgenstein and Russell, is that Russellian particulars were indubitable existents, whereas Tractatus objects were necessary existents. They were, as Wittgenstein later averred, what he could refer to without running the risk of their possible nonexistence (PR 72). But he eliminated that risk by metaphysical postulation, not by appeal to resistance to Cartesian doubt.3 (vi) Like Russell, Wittgenstein held that there is an external relation between names and objects. Words are things (or classes of things (cf. TLP 3.203)). They can stand in genuine relations to other things. To assign meaning to names is to correlate names and objects. This relation is effected in use — for one uses a name to mean an object, the method of projection being the intention with which the name is used (MS 108 (Vol. III), 218f.; MS 145, 49). The name-relation is also opaque. It is not self-evident what the objects are, hence not self-evident whether any given expression is a name. Wittgenstein later saw himself as having been committed to the view that future analysis would reveal what the objects and atomic propositions are (WWK 182f ). What is self-evident is that there must be names (and objects). 3

Metaphysical postulation, as Wittgenstein later realized, is but the bogus metaphysical analogue of explanatory theoretical postulation characteristic of the advanced physical sciences.

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(vii) Like Russell, Wittgenstein held that names are primitive signs. They resist analysis (TLP 3.26, 3.261). In this respect they contrast with ‘sentenceconstituents that signify complexes’. These latter must either be (deﬁnite) descriptions of a complex or abbreviations of such descriptions. In either case such symbols will disappear on analysis (TLP 3.241). However, on Wittgenstein’s view, whether a symbol can be broken down by analysis has nothing to do with epistemology. It is a matter neither of immunity to Cartesian doubt nor of whether it is certain that what it denotes exists. It is a purely logical issue. What can be analysed can be deﬁned. The deﬁnition states the essence of the complex. Under Wittgenstein’s presumption that all expressible necessity is logical necessity (TLP 6.37, 6.375), if something has a statable essence, then the symbol standing for it can be deﬁned, i.e. analysed. Therefore the indeﬁnability of names is the expression of the thesis that the essence or form of an object cannot be stated, only shown; that internal properties are ineffable (cf. TLP 2.0233, 2.02331). (viii) Simple symbols, i.e. names, are indeﬁnable. They are explained by elucidations. Elucidations of primitive signs are precisely parallel to Russellian explanations of ‘primitive ideas’. For they are propositions that contain the primitive signs (TLP 3.263). From them one is supposed to gather the meaning of the simple name (see ‘Ostensive deﬁnition and its ramiﬁcations’, sect. 1; cf. PR 54; see Exg. p. 18/16n.). (ix) According to the Tractatus, what is symbolized by a name can be symbolized only by a name. ‘Objects can only be named’ (TLP 3.221). Conversely, ‘Situations can be described but not given names’ (TLP 3.144). Pace Frege, sentences are not names; in particular, they are not names of facts (NB 97f., 102). (x) Wittgenstein agreed with Russell that ordinary proper names, which do not stand for simple objects that are part of the substance of the world, are not logically proper names at all. He apparently took it for granted that they would be eliminable on analysis by means of some variant of Russell’s Theory of Descriptions (cf. PG 211, quoted in Exg. §90). (xi) There is no reason to suppose that Wittgenstein held ‘this’ or ‘that’ to be proper names at all, let alone the sole logically proper names. On the contrary, his remark that the concept ‘this’ is identical with the concept of the object (NB 61) suggests that he would have denied this Russellian claim. For this remark suggests that ‘this’ is, in some sense, a formal concept indicating the general form of an object.

3. The criticisms of the Investigations: assailing the motivation The Investigations criticizes the conception of a logically proper name. Both Wittgenstein and Russell had radically misconstrued the role of names. Names, grammatically speaking, appeared not to be the real thing — they seemed raw,

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adulterated, defective. So Wittgenstein and Russell, in their endeavours to grasp the putative foundations of language, had sublimated the ordinary concept of a proper name (e.g. ‘Socrates’) and the ordinary concept of a name. They had a preconception about what a ‘real’ name ought to do. Consequently, while striving to grasp and describe the functioning of language, they had ended up denying that anything ordinarily conceived to be a name was really a name (for Wittgenstein’s later characterization of the process of sublimation, see ‘Turning the examination around: the recantation of a metaphysician’, sects 3f.). Indeed, in Russell’s case, the depth of confusion was reached in the claim that the only genuine names were expressions that are patently not names at all (PI §§38f.): namely, ‘this’ and ‘that’. Wittgenstein’s later criticisms do not ﬁnd fault merely with logical atomism. Instead, he attacks the presuppositions that lead one to sublimate our ordinary concept of a name into the illusory logically proper name. These presuppositions reach back as far as Plato — hence the quotation from the Theaetetus (PI §46). The thought that reality is analysable into simple constituents (or ‘simple natures’), and that all destruction is decomposition of complexes informed Descartes’s metaphysics and his proof of the immortality of the soul. The idea that names stand for ideas in the mind that are either simple or complex, and that the latter are deﬁnable and the former indeﬁnable informed classical British empiricism. So, while the errors of logical atomism are in the forefront of Wittgenstein’s criticisms, the signiﬁcance of his criticisms reaches much farther than a passing phase in early twentieth-century philosophy (see ‘The Augustinian conception of language’, sect. 2). Russell’s search for logically proper names was to a large extent motivated by the dual goals of ensuring the foundations of language in indubitable existents and of giving secure foundations to empirical knowledge in general. The foundations of language were conceived to lie in logically proper names that indubitably have a meaning, that can be known with certainty not to involve any reference-failure, that do not signify mere ﬁctions or logical constructions, but, as it were, unquestionably make contact with reality. What was thus resistant to the acids of Cartesian doubt seemed ﬁt to provide the foundations of empirical knowledge. In seeking to identify the particulars that are the meanings of logically proper names, Russell was also pursuing a traditional epistemological inquiry, but describing it in novel terminology. In advocating that particulars are currently experienced sense-data, he was at the same time also giving a familiar solution to this problem. The Investigations elaborates criticisms of the search for foundations of language. It explicitly repudiates the classical empiricist foundations that Russell advocated. The private language arguments undermine the idea that associating a name with a sense-datum can sufﬁce to endow it with meaning. Equally, the idea that a name can be given a meaning by private (mental) ostensive deﬁnition by reference to a sense-datum used as a private sample is shown to be incoherent (see Volume 3, ‘The private language arguments’ and ‘Private

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ostensive deﬁnition’). The idea that one knows with complete certainty that one is apprehending a current sense-datum — that, for example, it is indubitable that it seems to one just as if one is perceiving something white — is assailed by Wittgenstein’s account of avowals of experience. It is true that one cannot doubt that it seems to one just as if one is seeing something white. But doubt is not excluded here by knowledge, it is excluded by grammar. It makes no sense to doubt; but by the same token it makes no sense to be certain. So too, where it makes no sense to be ignorant, it also makes no sense to know. Avowals of immediate experience are misconstrued as reports of incorrigible truths (see Volume 3, ‘Avowals and descriptions’). In the sense that Russell had in mind, language has no foundations. Its roots do not lie in simple names signifying evanescent data of sense. Meaning is not, as it were, injected into the web of language by means of logically proper names that make contact with indubitabilia. In the sense in which language does have foundations, its foundations are in action — in common human reactions and responses. Hence ‘. . . and write with conﬁdence: “In the beginning was the deed”’ (Goethe, Faust, Part I, quoted C §402; also MS 119 (Vol. XV), 146f.). There are indeed things we cannot doubt on pain of radically disrupting the whole of our noetic structure, things that constitute ‘the inherited background against which [we] distinguish true and false’ (C §94). But far from being propositions about sense-data, they are propositions about the world around us and about ourselves and others in it, propositions such as ‘the world has existed for a long time’, ‘human beings have forbears’, ‘cats don’t grow on trees’ (C §282). And far from constituting foundations from which all else is derivable, these propositions are more akin to the keystone of an arch, inasmuch as they are held in place by everything else that we know and believe. The logico-metaphysical motivations of the Tractatus’s commitment to logically proper names are likewise assailed. It had seemed that names must ‘reach right up to reality’, in order to ensure the necessary ‘harmony between language and the world’. It appeared that the real names must have as their meanings sempiternal objects constituting the substance of the world. For it seemed as if only this would ensure that when one asserted things to be thus-and-so, and what one asserted was false, then things were not thus-and-so (‘if I say falsely that something is red, then all the same what it isn’t is red ’ (cf. PI §429 and Exg.)). It seemed as if the possibility of propositions being false but meaningful could be ensured only if the proposition is isomorphic with what it depicts truly or falsely. And that in turn seemed possible only if the constituent names in a proposition shared a common form with their meanings, conceived of as indestructible objects constituting the substance of the world. But this was illusion. The apparent harmony between language and reality is forged in grammar — not between grammar and reality. That the proposition that p is the proposition that is made true by the fact that p and also the proposition made false by the fact that not-p is not an ineffable metaphysical truth, but a pair of grammatical propositions concerning the intersubstitutability of propositions:

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‘the proposition that p’ = ‘the proposition made true by the fact that p’ ‘the proposition that p’ = ‘the proposition made false by the fact that not-p’

It is all done in language (see Volume 4, ‘Intentionality’). But to ensure this intersubstitutability of expressions, there is no need to postulate the existence of sempiternal simples. Ordinary names can be said to ‘reach right up to reality’, for they are not disguised deﬁnite descriptions. But the objects that they reach right up to are not sempiternal simples. They are all manner of different things and kinds of things that we name. Such nominata are not necessary existents. Nor are they the meanings of names. It had also appeared that simples had to be postulated as the meanings of the real names in order to ensure determinacy of sense. It had seemed that determinacy of sense had to be ensured if language is to be, as it must be, ‘in good logical order’. Only if the unanalysable names that are the constituents of elementary propositions have simple sempiternal objects as their meanings is it assured that each such proposition is bipolar, that it divides logical space precisely into two (allowing for no vagueness), and that it is immune to reference-failure. Then, given that all propositions are generated out of elementary propositions by the operation of joint-negation, we can be assured that any apparent indeterminacy is determinately indeterminate and will disappear on analysis. But, as Wittgenstein now realized, the very conception of determinacy of sense is incoherent. Language is indeed in good logical order, but this does not imply that all vagueness is merely apparent. Nor does it imply that even the mere possibility of vagueness can be excluded by linguistic rules. So the (ineffable) existence of simple sempiternal objects is not presupposed by the possibility of representation by means of language. It had appeared that the nominata of ‘real’ names must be necessary existents as a condition of the possibility of linguistic representation. But, Wittgenstein later realized, that was an illusion. ‘What looks as if it had to exist, is part of the language’ (PI §50). Of course, the nominata of ordinary names do not, and were not thought to, signify sempiternalia that constitute the substance of the world. But this had merely sent Wittgenstein on the quixotic quest for the nominata of real names. The best candidates appeared to be such things as perceptual qualities or fully analysed perceptual qualities (cf. PI §87). For it seemed that red (dark, sweet) or shades of red (degrees of darkness or of sweetness) must exist in order for one to be able to say either that A is red or that A is not red. And surely one cannot destroy red! But what seemed to be the simple objects of which reality is made are no more than samples that belong to the method of representation (see ‘Ostensive deﬁnition and its ramiﬁcations’, sect. 6). They are part of the symbolism. They are eminently destructible; they do not have to exist. But, to be sure, if a given sample did not exist (and we could not reproduce it), then the word we deﬁne by reference to it would have no meaning or a different meaning. We are indeed tempted to say that red cannot be destroyed (you can destroy red things, but

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not red itself ). But all this means is that the word ‘red’ has a meaning — which is standardly explained by reference to a sample of red (PI §§55, 57).

4. The criticisms of the Investigations: real proper names and simple names In addition to the very general criticisms of the deep motivations that underlay his and Russell’s misconceptions of logically proper names, Wittgenstein also gave detailed criticisms of more speciﬁc misconceptions, both regarding proper names (properly and non-‘logically’, so called) and regarding names of ‘simple’ qualities. His criticisms of what he and Russell had conceived of as logically proper names presuppose his later conception of ordinary proper names and their roles. This conception is questionable. For he equates explaining who N is with explaining the meaning of N’s name ‘N’. This commits him to a number of substantial claims which are problematic. These are not questioned in this essay, but deferred until later (see ‘Proper names’, sect. 7). (i) Wittgenstein continues to assert the contextual dictum that a word has meaning only in the context of a sentence (PI §49). This contradicts Russell’s claims about logically proper names. It is in apparent agreement with the Tractatus. But, with the abandonment of the picture theory of representation, Wittgenstein’s interpretation of the dictum is now profoundly different. Indeed, the picture-theoretic interpretation of this dictum in the Tractatus cannot consistently be carried over into the Investigations; nor is the gloss given it in the Investigations consistent with its signiﬁcance in either the Tractatus or Frege’s writings. (See ‘Contextual dicta and contextual principles’, sects 1–4.) (ii) The meaning (Bedeutung) of a real proper name is not its bearer, the object named (PI §§40–3). For most uses of the expression ‘the meaning of a word’, it can be explained as ‘the use of a word’. In the case of ordinary proper names, we sometimes explain what the name ‘N’ means (sic), or better, who or what N is, by pointing to the bearer of the name (PI §43). But of course the bearer of the name is not to be construed as being the meaning of the name. Rather, by pointing to the bearer, we explain how the name is to be used (namely, as the name of that person or object, to call, address or refer to the person, to pick out the object and ask for it or to identify it or describe it, and so forth). Wittgenstein advanced two arguments to show that the meaning of a real proper name is never its bearer. First, loss or destruction of the bearer of a name ‘N’ does not deprive the name of meaning (of its use). When a person dies, his name soldiers on (PI §40); it is used to talk about him, to ask questions about him, to describe him and his life. Secondly, a name ‘N’ which has never had a bearer may have a use or meaning (PI §42). One might add that it may be perfectly clear that a name has a use even though we cannot determine whether it has (or ever had) a bearer (e.g. ‘Homer’), and also that it has

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a use when we know it has no bearer, e.g. ‘Vulcan’ (the supposed intraMercurian planet). (iii) Grasping the use of an ordinary proper name need not involve acquaintance with the bearer (or the relevant bearer, if the name has more than one bearer). Even if it does involve such acquaintance (as in being introduced to Mr N), it does not consist in acquaintance with the bearer. To understand an utterance incorporating the name ‘N’ does not require knowing N, but rather knowing who (or what) N is. There are various criteria for such knowledge (see ‘Proper names’, sect. 4). The related atomist thesis that ‘understanding’ of a logically proper name is independent of the knowledge of any truths about its bearer, if applied to actual proper names, conﬂates various points, some true and some false.4 If read as the claim that giving a description of N never constitutes a criterion for knowing who N is, it is false. There is a grammatical connection between giving appropriate descriptions and knowing who N is (who is referred to in an utterance ‘ΦN’). On the other hand, this connection is not an entailment. Therefore, if the atomists’ thesis is read as the denial that giving any description of N entails that the speaker knows who N is, it is true. Finally, if read as a version of the logical thesis that satisfying a given deﬁnite description is never either logically necessary or logically sufﬁcient for being N, then it may be acceptable. For it seems at least compatible with the proposition that giving a description of N is a criterion for knowing who or what N is that there is no grammatical connection between satisfying this description and being N. (iv) The insertion of an ordinary proper name in the sentence frame ‘ξ exists’ or its negation does not typically yield a meaningless sentence, although in some contexts it is a needlessly obscure way of making perfectly clear statements. The sentence ‘Moses did not exist’ is perfectly in order (PI §79), and people have carried on serious arguments about whether Homer existed, whether Jehovah exists, and whether Vulcan exists. Not only are such sentences in order, but also, in Wittgenstein’s view, they may mean different things (PI §79) and be explained in different ways. Neither ‘N exists’ nor its negation makes a statement that is necessarily true. There are three main roots to the atomist misconception that a sentence of the form ‘N exists’ is meaningless where ‘N’ is a proper name. The ﬁrst is the mistake of identifying the meaning of a name with its bearer. It then seems that ‘N does not exist’ must be meaningless, since if N does not exist, then ‘N’ has no meaning, and if ‘N’ has no meaning, then ‘N does not exist’ has no meaning. Given the further idea that the negation of a sentence with a meaning must also have a meaning, and the negation of a meaningless sentence must also be meaningless, it is easy to see why one might hold that ‘N exists’ is also meaningless. The second root concerns the thought that one can 4 It should be noted how stilted and misleading it is to speak of understanding a proper name of a person or place, as opposed to knowing who or what is named by it.

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name only objects of acquaintance, and that the fundamental form of such naming is by the use of the demonstrative in the sentence form ‘This is . . .’. It might appear to follow from the nonsensicality of ‘This exists’ (except in very special circumstances) that sentences of the form ‘N exists’ are also nonsensical. But even if that is correct, it is quite wrong to think that names are always explained ostensively or, indeed, that only objects of acquaintance can be named. The third root is the mistake of projecting the form of representation of the predicate calculus on to ordinary language. Dummy names cannot occur as arguments of quantiﬁers in the calculus. But to infer from this that one cannot legitimately say that Vulcan does not exist would be erroneous. (v) There is no such thing as the name-relation. There are many different relations of names to objects (PI §37; BB 172f.). Even if there were a single relation of naming, it would be neither external nor opaque. That ‘N’ is the name of (or ‘stands for’) N is not a truth of psychology (BB 3), but a truth of grammar. It may be interpreted simply as an instance of the schematic formula ‘ “x” is the name of x’. The schema expresses a grammatical truth. Every substitution-instance of it is true in virtue of the conventions for the use and mention of names and of the meaning of ‘is the name of ’. Consequently, a substitution-instance of it will be recognized as a grammatical truth even by a person who does not know the meaning of ‘N’, at least if he knows that ‘N’ is a proper name. So the sentence ‘ “N” is the name of N’ expresses an internal relation between a proper name and an object. By and large, it can be established with certainty whether or not an expression is a genuine proper name. Whether it is or not depends merely on how we use it and how we explain its use, not on any kind of research, scientiﬁc or philosophical, into what it refers to. There is no such thing as discovering, contrary to our previous opinion, that what we all thought to be a proper name is in fact not a proper name at all. No mystery enshrouds the notion of a proper name; there are no deep problems to be solved in deciding which expressions are proper names, although there are borderline cases. Furthermore, there is no general distinction between what speakers of a language take ‘N’ to refer to and what ‘N’ (really) refers to. There are no transcendent questions about references, although of course we may remain ignorant about Homer’s or King Arthur’s existence. (vi) The atomist claim that logically proper names cannot be analysed is approximately correct for ordinary proper names in one respect. Typically, there are no conditions logically necessary and sufﬁcient for an object’s being N, where ‘N’ is a proper name. Consequently, ordinary proper names cannot be analysed as abbreviations of deﬁnite descriptions even where they are explained by descriptions. Their explanations also take other forms. On the other hand, it is not a consequence of this that there are no criteria for correctly grasping the use of a proper name. In particular, it does not follow from the fact that a typical name ‘N’ is not logically equivalent to any deﬁnite description that giving a description which in its context individuates

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N is not a correct explanation of who N is and hence a criterion for understanding ‘N’. Denial that names can be analysed is independent of denial that their use can be explained. (vii) Whatever limited truth there is in the claim that proper names are simple symbols (see ‘Proper names’, sect. 6), this alleged simplicity does not entail either that the use of such names cannot be explained or that there are no criteria for knowing who or what N is. (viii) The atomist thesis that what is symbolized by a name can be symbolized only by a name seems primarily intended as an alternative formulation of the thesis that names cannot be analysed. It just asserts that the role of names differs from that of deﬁnite descriptions. This is true, but it does not have the dramatic implications the atomists took it to have. In particular, it does not justify the absurd claim that what is named cannot be described. (ix) The distinction between ordinary proper names and logically proper names is misguided. The class of logically proper names is empty, and hence the logic characteristic of logically proper names is a logic for a vacuum. The counterpart contention that most ordinary proper names are incomplete symbols is false. Distinguishing ordinary proper names from logically proper names is doubly mistaken. It mischaracterizes ordinary proper names in claiming that they can be ‘analysed’, and it misleads by suggesting that the set of logically proper names is not empty. (x) Demonstratives are quite distinct from names. To assimilate them to names, or to conceive of them as the only genuine names from a logical point of view, is to ignore the important logical differences between demonstratives, names and proper names. (See ‘Indexicals’, pp. 110f.) Of course, neither Russell nor the young Wittgenstein, in their discussions of logically proper names, were attempting to account for the ways in which grammatically proper names function. Russell gave an explicit account of such names elsewhere, and Wittgenstein apparently accepted it with only minor qualiﬁcations. The entities named by what they thought of as logically proper names were, in Russell’s case, evanescent sense-data, and, in Wittgenstein’s case, such things as shades of colour, tones or, more generally, minima discriminabilia. But here too the account was incoherent. Some of Wittgenstein’s later criticisms are discussed in ‘Ostensive deﬁnition and its ramiﬁcations’, sect. 6. Here it is worth drawing attention to the extent to which names of perceptual qualities still fall short of the requirements the Tractatus placed on simple names. ‘Red’ (or the name of a shade, such as ‘scarlet’) can be said to be a name. It has both a nominal and an adjectival use (‘Red is my favourite colour’ and ‘She has red hair’). But even in its nominal use it is obviously not what we ordinarily conceive to be a proper name. Furthermore, the colour it signiﬁes is not a simple object. Nor is it a complex object. It is not an object at all. Moreover, ‘simple’ and ‘complex’ are not predicative adjectives but attributive ones. So simplicity and complexity are not absolute but relative properties,

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and criteria of simplicity and of complexity have to be laid down for each context (PI §§47f.). It is indeed tempting to say such things as ‘Red cannot be described’, but that is misleading. If it means that one cannot describe (i.e. there is no such thing as describing) a quality in the manner in which one describes a substance (viz. by specifying its qualities), then there is some truth to the claim. But, of course, one can ‘describe’ red as ‘the colour of blood’; or, differently, as the complementary colour to green, or as the colour one gets when pink gets darker and darker. One may indeed say that ‘red’ is unanalysable; we may even claim (misleadingly) that it is indeﬁnable. But all that this amounts to is that we do not deﬁne the word ‘red’ by an analytic deﬁnition. Rather, we explain what the word means by an ostensive deﬁnition by reference to a sample. But the meaning of the word ‘red’ is not the sample pointed at in explaining what ‘red’ means; nor is it the object pointed at in saying that A is red. The sample, as has been made clear, is an instrument of language and belongs to the means of representation. We explain what ‘red’ means by pointing to a sample. ‘This colour + n’ (pointing at a red sample) can be substituted for the word ‘red’ in a sentence (e.g. ‘My curtains are red’), just as a deﬁniendum can replace the deﬁniens. The ostensive deﬁnition does not connect word and world, language and reality. It is a rule for the use of the word deﬁned. One may say that red cannot be destroyed. But all this means is that it makes no sense to say ‘Red is destroyed’. But it makes perfectly good sense to say that everything that is red has been destroyed. And if there are no possible samples by reference to which to explain a word that is deﬁned by reference to a sample, then that word will indeed cease to have a meaning or assume a different meaning (PI §57). One can say such things as ‘there is such a colour as Cn’; it is just to say that the colour name ‘Cn’ has a meaning. One might further say ‘Cn exists’, but all that this means is that there is something that has that colour (PI §58). Of course, it would be absurd to suppose that there is any such thing as a ‘name-relation’ between a colour-name and the colour of which it is a name, and even more absurd to suppose that it is established by some mental act. What makes the name of an ostensively deﬁned colour into a colour-name are the ways in which it is used and the ways in which it is explained, and neither of these is a psychological matter. In short, the logical atomist investigations into logically proper names distorted the logico-grammatical character of names of simple qualities no less than it distorted the ordinary concept of a proper name.

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

VIII

Meaning and use 1. The concept of meaning The concept of meaning is central to the concerns of the Philosophical Investigations. It is multifaceted, and linked in various ways to other concepts. The purpose of this essay is to give a synoptic view of Wittgenstein’s reﬂections on meaning and use, to clarify what he meant by ‘use’, and to mitigate some qualms about his association of the concepts. This overview is supplemented by other essays in this Commentary, in particular ‘The Augustinian conception of language’, ‘Explanation’, ‘Descriptions and the uses of sentences’, ‘Ostensive deﬁnition and its ramiﬁcations’, and ‘Understanding and ability’ in this volume; ‘Rules and grammar’, ‘Following rules, mastery of techniques and practices’, and ‘Grammar and necessity’ in Volume 2; ‘Intentionality’, ‘The arbitrariness of grammar and the bounds of sense’, and ‘The mythology of meaning something’ in Volume 4. These essays dig much deeper into his treatment of some of the topics raised here. Attaining an overview of his conception requires a grasp of the location of the concept of meaning in the web of related notions. So I shall ﬁrst sketch the semantic ﬁeld within which it is embedded. I shall then elaborate the desiderata that any cogent account of linguistic meaning must satisfy. Wittgenstein’s reﬂections will then be described. Finally, some of the problems arising out of his qualiﬁed identiﬁcation of the meaning and the use of expressions will be scrutinized. Natural meaning is distinguishable from non-natural meaning (VoW 89, using the terms ‘indication’ and ‘sign’) — a distinction that goes back to the Cratylus and is elaborated in Augustine’s On Christian Doctrine. Natural meaning is in question in such observations as ‘Smoke means ﬁre’, in which we allude to an evidential correlation. Here one thing signiﬁes, is a natural sign of, another thing, as rain-clouds are a sign of impending rain. Non-natural meaning may be linguistic (verbal) or non-linguistic. The latter is exempliﬁed by conventional signs and signals, e.g. shop signs, trafﬁc lights, conventional gestures, uses of icons on modern electronic gadgetry. If that sign hangs outside a shop, this means or signiﬁes that it is a pawnbroker’s shop — the sign is a sign for a pawnbroker’s. If the trafﬁc light turns red, or if a trafﬁc policeman holds up his hand thus, that means one has to stop — it is a signal to stop. Rather differently, non-natural meaning is exempliﬁed iconographically in the arts, both by convention and at the artist’s choice. Iconographic conventions in painting

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determined, for example, that if a ﬁgure in an altarpiece is holding a palm leaf, this meant that the person depicted is a martyr; a man walking in a landscape holding a large ﬁsh conventionally meant that he is Tobias, and if he is holding the hand of an angel, this signiﬁed that the angel is Raphael. Sometimes iconographic meaning may be partly pictorial and partly linguistic. If asked what the wasps in Botticelli’s Venus Conquering Mars mean, we may explain that this is a visual pun on the family name of the Vespucci, for whom the painting was made. We are also familiar with meaning in representational music. For example, the closing bars of Till Eulenspiegel mean, signify, that the spirit of Till lives on; the rolling drums in La Symphonie Fantastique signify the impending execution in the dream. So, meaning is associated with signiﬁcance. We may ask after the signiﬁcance of footprints in the sand, of the curious sign outside a shop, or of the dramatic opening bars of Thus Spake Zarathustra. Rather differently, we speak of the meaning and signiﬁcance of a ritual (a Christian baptism) or rite within it (immersion). Meaning qua signiﬁcance is also linked to values and valuations, as when we speak of the meaning (or meaninglessness) of life, or of the ethical meaning of a person’s deed, or when we refer to the meaning that something may have in our lives. Linguistic (verbal) meaning is at issue when we speak of the meanings of words, where the question of what a given word means, or signiﬁes, i.e. is a word for, can be raised. The word ‘perambulate’, we may explain, is a word for an activity; it means to walk, or means the same as ‘to walk’. Words may have a meaning (‘lily of the valley’) or lack a meaning (‘Lillibullero’); two words in the same language (‘perambulate’ and ‘walk’) or in different languages (‘red’ and ‘rot’) may have the same meaning. We explain what a word means by giving a deﬁnition, or by an ostensive explanation, by contextual paraphrase or contrastive paraphrase, and so on. In so doing we give or specify the meaning of a word, but do not describe the meaning, just as we give or specify the weight, height, colour or price of an object, the date and time of an event.1 We look up the meaning of a word in a dictionary, ask what a word means, learn and later forget what it means; we may memorize the meanings of technical expressions in a science or craft, understand, fail to understand or misunderstand the meaning of a certain word in a given context. Word-meaning is linked to sentence-meaning, for words are parts of speech and contribute to the signiﬁcance of any sentence in which they may occur, and hence to the determination of what is said by its use. The meaning of a sentence must indeed be distinguished from what is said by the use of the sentence on a given occasion, although the former partially determines the latter. What is said by the use of a sentence may be true or false, wise or foolish, but the meaning of the sentence can be none of these. Note that unlike 1

But, of course, we may describe the meaning of a given word as difﬁcult to explain, as we may describe the colour of an object as difﬁcult to match.

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the case of word-meaning, where we can say that ‘W’ means a G that is H (‘bachelor’ means an unmarried man), we cannot, in the case of sentences, engage in comparable metalinguistic descent of the form: ‘ “N.N. is perambulating” means that N.N. is taking a walk.’ For the sentence does not mean any such thing. What may mean that N.N. is taking a walk is the fact that it is 3 o’clock and his hat and walking stick are missing from the hall. The sentence ‘N.N. is perambulating’ means the same as ‘N.N. is taking a walk’, but neither the sentence nor its utterance mean, signify, that N.N. is taking a walk. But, of course, A, uttering the sentence ‘N.N. is perambulating’ typically means by that sentence that N.N. is taking a walk. So, what a word or sentence means and what a person means by using a word or uttering a sentence are obviously linked. Being derived from the Old High German ‘meinunga’ (from which ‘meinen’) and Old English ‘mænan’ (‘to intend’), ‘meaning’ (unlike the German ‘Bedeutung’, which is connected to pointing (deuten)) is interwoven with the psychological concepts of intending or having in mind, and hence with the purpose a person may have in speech and deed. For we speak of someone’s meaning such-and-such a thing by a word. We explain what a speaker meant by the sentence he uttered, typically by giving a paraphrastic explanation of his utterance. We may further explain what he meant by what he said (i.e. by what is expressed by his utterance of that sentence), commonly by spelling out the implications that he had in mind. We also speak of what someone meant (intended) to say (but didn’t). And the idea of a person’s meaning something by his word or words is linked to the notion of a person’s meaning what he said, i.e. being serious about it, not speaking in jest. This essay is concerned with the conventional meaning of words and sentences. The concept of the conventional meaning of a linguistic expression is linked with others. The meaning of a word is connected with the notions of what the word applies to, what it signiﬁes, what it represents, and what it is a word for. So it is also linked with standing for something and naming something — a linkage the misunderstanding of which lies at the heart of the Augustinian (mis)conception of language. Since different words may have the same or related meanings, as well as contrary meanings, the meaning of a word is linked to the ideas of synonymy and antonymy. As noted, what a word means is linked to what a sentence in which it occurs means, and that in turn with what is said by its use, i.e. in the case of declarative sentences, to the proposition (if any) it expresses in use or to the statement (if any) that is made by its use. Since propositions and statements are true or false, the concept of the meaning of a word is mediately connected with the concepts of truth and falsehood. For what a constituent word in a propositionexpressing or statement-making sentence means contributes to the determination of what must be the case if the proposition expressed or statement made is to be true. This nexus, that characterizes a wide range of declarative sentences, dominated philosophical reﬂections on word- and sentence-meaning

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throughout much of the twentieth century. The later Wittgenstein, with reason, placed no emphasis on this connection. The meaning of a word may also contribute to the determination of the speech-acts that are performed by uttering a sentence in which it occurs. Although it is mistaken to explain what a give word means by reference to the speechact that might be performed by the utterance of a sentence that incorporates that word (e.g. ‘good’ or ‘bad’), there may be an internal relation2 between what a certain word means (e.g. its thus signifying a value or disvalue) and what is done in predicating it of something in a simple assertion (e.g. commending or condemning). For we explain the latter in terms of the former. The concept of the meaning of an expression is connected with that of explanation of meaning or (perhaps more felicitously) with an explanation of what the expression means, hence too with that of deﬁnition (since a deﬁnition is one way of explaining what a word means), and with that of a rule for the use of a word (since a deﬁnition or, more generally, an explanation of what a word means gives a rule for the correct use of a word). And since what a word means is connected with the point of invoking it, the concept of meaning is also linked with the concept of the general purpose of a word, which is speciﬁed by answers to the question ‘Why do we need this word in the language?’ or ‘What job does this word do?’ Moving off in a different direction, meaning is connected with the grounds or justiﬁcation of application, and hence too with evidence, in particular with criteria (a priori evidence) and veriﬁcation. For in many cases, what an expression means is not logically independent of the grounds for its application or of what would verify its application. It is patent, for example, that dispositions, powers and abilities, such as fragility and solubility, being able to see or hear, knowing or understanding, are not merely inductively connected with the manifestations or exercises of those dispositions, powers and abilities that provide grounds for their ascription. Since sentences are uttered with understanding by speakers, and heard and understood by their hearers, what a word or sentence means is bound up with the concept of understanding (misunderstanding and not understanding), and with that of interpreting. For what is understood when the utterance of another is understood is what the sentence he uttered means, what he said, and what he meant by it. By and large, if one does not know the meanings of the constituent words in a person’s utterance, one will not, save by guessing, understand the sentence uttered, or what was said by uttering it.3 Since a sentence 2

An internal relation is a relation the obtaining of which is a condition of the identity of the relata, and so partly constitutive of the meaning of the words signifying the relata, e.g. red’s being darker than pink or 3’s being greater than 2. 3 Of course, that does not mean that if one does understand what someone has said, then one has derived the sense of his utterance from the meanings of the words in the sentence he uttered and their mode of combination. For discussion of this ‘computational’ conception of understanding sentences and what is said by their use, see ‘Contextual dicta and contextual principles’, sect. 6.

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may admit of more than one meaning, interpretation may be called for to determine what is said by its use in a given context. These conceptual connections were a salient preoccupation of twentieth-century philosophers (and linguists), and a source of extensive misconceptions. A philosophical investigation into linguistic meaning should give us a surveyable representation of the concept by arranging the ‘grammatical’ data (in Wittgenstein’s generous sense of the term ‘grammar’) in a manner that clariﬁes and illuminates these manifold connections. However, philosophical thought does not take place in a vacuum. The stage is set by problems and puzzlement. The action proceeds under the inﬂuence of a variety of preconceptions. Particular problems or puzzles have induced philosophers typically to focus sharply on a small number of internal relations, commonly in relative disregard of the rest of the complex network. Idealist conceptions of language and linguistic meaning that dominated philosophy from Bacon, Hobbes, Arnauld and Locke to the end of the nineteenth century conceived of language primarily as a vehicle for the communication of thoughts and judgements, which were in general held to be independent of language.4 Judging was conceived to be a matter of combining ‘ideas’ (in the cases of afﬁrmations) or separating ideas (in the case of denials) of subject and predicate. Thinking or reasoning was accordingly conceived to be the transposition of relations of ideas. Eager to validate, or limit, knowledge claims in the face of scepticism, seventeenth- and eighteenth-century philosophers tended to focus on the source of ideas. The empiricists cashed word-meaning in the currency of ideas derived from experience, and accordingly determined a general principle of signiﬁcance (vide Hume). The rationalists insisted on the innateness (actual or virtual) of (at least categorial) ideas. The tide turned against linguistic idealism and psychologism at the end of the nineteenth century. In the twentieth century, accounts of meaning inspired by Frege, the Tractatus and Tarski, and driven by the conception of a language as akin to a calculus, tended to focus on the interpretation of the alleged calculus of language in terms of truth-conditions of sentences, cashing word-meaning in terms of the contribution of a word to the determination of the truth-conditions of any sentence in which it may appear.5 The logical positivists, inspired by Wittgenstein, but preoccupied with the ‘logic of science’, focused upon the connection between meaning and veriﬁcation, and meaningfulness and

4

There were, to be sure, exceptions, who took a very different line, e.g. Vico, Condillac and Herder in the eighteenth century, and the German hermeneutic tradition in the nineteenth. Nevertheless, idealist conceptions of meaning dominated reﬂections on language from the seventeenth century to Mill and the German psychological logicians. 5 In a ﬁt of nominalist fervour, sentences were misguidedly conceived to be bearers of truthvalues. It is not sentences that can be true or false but what is said by the use of a (declarative) sentence.

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veriﬁability.6 Behaviourist theories of meaning (Ogden and Richards, Charles Morris) in the ﬁrst half of the twentieth century, motivated by the goal of reducing meaning to behaviour and behavioural dispositions, focused upon the causes of and responses to utterance. Intentionalist (Gricean) conceptions of meaning, driven by the hope of deriving semantics from psychology, focused upon the connection between the meanings of words and sentences and speakers’ communication intentions. Such highly selective vision has, at best, meant that only a small number of internal relations that characterize linguistic meaning were described, and the remaining relations were left to take care of themselves. At worst (as in the case of truth-conditional semantics) it has meant that internal relations between a select set of elements were delineated in a manner incompatible with an adequate account of the other internal relations, thus guaranteeing distortion or falsiﬁcation (see ‘Descriptions and the uses of sentences’). Furthermore, the preconceptions have determined what were thought to be the possible resolution of the problems as they were apprehended. It is evident that Wittgenstein thought that many of these preconceptions were moulded by tacit or explicit adherence to the principles of the Augustinian conception of language. This is true of twentieth-century reﬂections on meaning no less than of seventeenth-century idealist ones. Twentieth-century philosophy was preoccupied with formal and informal semantics. This preoccupation was stimulated by the invention, at the turn of the century, of the new logic of Frege, Russell and Whitehead. Confronted by the power and perspicuity of the predicate calculus relative to syllogistic and logical algebra, it was virtually unavoidable that philosophers, including the inventors of the calculus, should raise the question of the relationship between the formal calculus and natural language. It seemed that the calculus was either a logically perfect language (Frege, Russell), against which the logical defects of natural languages can be judged and relative to which proposals for its improvement for ‘scientiﬁc purposes’ might be advanced (Carnap), or it disclosed for the ﬁrst time the depth grammar (or part of the depth grammar) of any possible language (the Tractatus and some theorists of meaning for natural language in the late twentieth century). The concepts of syntax and semantics were tailored to the apparent requirements of logical calculi, and the conception of pragmatics was invoked to budget for some of the differences between the truth-functional calculus and natural language. This reinforced the tendency to think along the tracks of the Augustinian conception of language. For, it seemed, the syntax of the calculus of logic and of a natural language alike is 6

It would be misguided to suppose that they were propounding a veriﬁcationist (‘anti-realist’) conception of meaning in opposition to a truth-conditional (‘realist’) one. On the contrary, they thought of themselves as espousing a truth-conditional conception of meaning, in which truthconditions are subject to empiricist constraints, and so limited to what is veriﬁable in experience. For discussion of this point, see Wittgenstein’s Place in Twentieth-Century Analytic Philosophy, pp. 50–9.

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concerned with the formation rules of the symbolism, i.e. with the conditions of well-formedness. Semantics, it seemed, dealt with the ‘interpretation’ of the symbolism, with the assignment of meaning to the elements of the symbolism, and so with the resultant determination of the meaning or sense of sentences. This was conceived to be a matter of correlating the signs of the symbolism with reality. Calculi were held to be given an interpretation by assigning objects to names, properties to monadic predicates, and relations to n-adic predicates.7 On this basis, it was supposed, rules can be speciﬁed in a metalanguage that determine truth-conditions for every sentence of the formal system. A striking feature of twentieth-century reﬂections on meaning is the extent to which philosophers were disposed to recognize only simple and rigid connections between concepts. There was a tendency to assume, for example, that evidence and veriﬁcation either straightforwardly determine the meaning of a sentence or they have nothing to do with its meaning. Either understanding what is said by the use of a sentence is knowing how to verify it, or else veriﬁcation is irrelevant to determination of meaning and of what is said. Either citing evidence speciﬁes the meaning or sense of any sentence for the assertion of which it is evidence, or that evidence is a mere symptom (inductive support) and irrelevant to the meaning or sense. Wittgenstein, by contrast, came to think that many of the conceptual connections in this domain are, in different ways, looser and more ﬂuid than this. For example, for some sentences, the way in which what is said by their use is veriﬁed is an aspect of, or partial determinant of, their meaning. For someone who had no idea how to measure time would not be said to grasp the concept of such-and-such a period of time; and so too, someone who had no idea as to what forms of behaviour provide grounds for saying of a person that he is in pain could not be said to have grasped the concept of pain. But, he urged, it does not follow that the meaning of every declarative sentence is given by speciﬁcation of its veriﬁcation conditions. Many sentences are licitly used without any grounds (e.g. ‘I’m going now’, ‘This is red’, ‘The world has existed for many years’). Furthermore, a datum may be a criterion (a priori evidence) for ‘p’ on one occasion (and so partly constitutive of its meaning) and a symptom on another. For it is characteristic of scientiﬁc concepts that there is a ﬂuctuation between symptoms and criteria (PI §354; cf. Z §438).8 In short, the instruments of language are very diverse. We tend to be deceived by superﬁcial uniformity 7

This conception of semantics as correlating the calculus with reality involved fundamental misunderstandings, as Wittgenstein noted in his criticisms of Russell, Ramsey and Carnap. In introducing n-place relations into the calculus and then looking for an interpretation, one is not, as it were, preparing language for reality (if there happen to be, say, seven-term relations in the world). One is preparing the calculus for a future grammar (if there happen to be seven-term relational predicates in our language). For we do not map the calculus on to reality in order to give it an interpretation, we map it on to our language (PG 309–14; AWL 142f.). 8 For an examination of this point and its relevance to the meanings of technical terms in science, see Wittgenstein’s Place in Twentieth-Century Analytic Philosophy, pp. 250–3, p. 329, n. 46.

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of appearances (e.g. ‘He has a pain’ and ‘I have a pain’ look alike, but display numerous ﬁrst-/third-person differences in respect of grounds of assertion, of the admissibility of epistemic operators such as ‘I know that’, ‘I wonder whether’, ‘I discovered that’, and of the relationship between truth and truthfulness), and to disregard differences of use and function (e.g. between ‘I don’t know what he wants’, which is a confession of ignorance, and ‘I don’t know what I want’, which is a confession of indecision) — as if we could apprehend only the handles of tools, disregarding the different kinds of things we do with them (cf. PI §§11f.). Craving uniformity and context-independent regularity, we overlook the ﬂuidity, ﬂexibility, forms of context-variability and distinctive uses of our language and its instruments. Similarly, reﬂection was commonly guided by what Wittgenstein came to think were dogmatic commitments. Philosophers were prone to think that explaining what a word means must take the form of correlating the word with an object, property or relation in the world (see ‘Ostensive deﬁnition and its ramiﬁcations’); or that it must take the form of stating the common properties of everything to which the word applies, i.e. of specifying conditions necessary and sufﬁcient for the application of the word (see ‘Family resemblance’). Nothing short of this would really do. So too, it seemed that giving a correct explanation of the meaning of a sentence (or of what is said by its use) must take the form of specifying its truth-conditions. But, Wittgenstein urged, one should ask oneself whence these musts, and examine what, in our ordinary linguistic transactions, we call ‘an explanation of meaning’ and what the role of an explanation of meaning is (see ‘Explanation’).

2. Setting the stage Throughout his later writings, Wittgenstein spelled out and argued for desiderata that any general account of linguistic meaning must satisfy. The concept of meaning must be so construed that different people can understand what the words of a language (and utterances made by their use) mean. Words need not be common property (vide the last Mohican), but it must be possible for them to be common property. This sharability requirement was not satisﬁed by Russell’s reﬂections on language in his logical atomist phase.9 The concept of word-meaning must ensure the possibility of ‘agreement in deﬁnitions’ (PI 9

He held that ‘When one person uses a word, he does not mean by it the same thing as another person means by it. I have often heard it said that that is a misfortune. That is a mistake. It would be absolutely fatal if people meant the same things by their words. It would make all intercourse impossible, and language the most hopeless and useless thing imaginable, because the meaning you attach to your words must depend on the nature of the objects you are acquainted with, and since different people are acquainted with different objects, they would not be able to talk to each other unless they attached quite different meanings to their words’ (PLAt 174). This deliberately excluded shared meaning.

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§242). This, pace Russell, is a prerequisite for communication by means of language. This requirement was not satisﬁed by idealist conceptions of meaning that characterized classical empiricism and nineteenth-century German psychologism and that were criticized by Frege in his anti-psychologist polemics.10 Wittgenstein’s arguments against the possibility of a private language (PI §§243–315) are intended to demonstrate that the assumptions that the meanings of words are ideas in the mind and that words can be assigned a meaning by association with an idea or by private ostensive deﬁnition are incoherent (see Volume 3, ‘Private ostensive deﬁnition’). Not only would what words mean be incommunicable, but further, the words a speaker utters would not be understood even by himself, i.e. they would not actually have any meaning at all. What words signify or stand for must be what speakers use those words to ask for, ask about, point out or talk about — which is primarily (though, of course, not exclusively) items in the objective world around them. In so far as we use sentences, inter alia, to describe how things are, the concept of the meaning of a sentence must be so construed as to make it possible that sentences can be used to state how things objectively are. It must be possible that by the utterance of a sentence with a given meaning, a speaker might mean that things are as he thus describes them as being. So language, and linguistic meaning, must, in this sense, be capable of reaching up to extra-mental reality. Far from all words being construed to be names of ideas (or ‘mental representations’), many words must surely be words for public objects, properties and relations. We may call this the objectivity requirement. This too was not satisﬁed by classical empiricists’ and psychologicians’ conceptions of meaning. The problem with which they struggled, with questionable success, was how to ensure the transition from the representation of ideas and their subjective relations to the representation of things and their objective relations. The concept of meaning must be such as to ensure a degree of constancy over time and regularity in application (PI §§207f., see Exg.). For words to have a meaning, they must be integrated into a practice. This is a condition for the existence of an internal relation between the explanation of a word (a rule for its use) and its application that is itself a condition for there being a distinction between a correct and an incorrect use. The constancy and regularity requirements were not satisﬁed by Russell’s reﬂections on meaning in his logical 10

Frege’s polemics were vitiated by his acceptance of the misconception of ideas that he shared with his adversaries. For, like them, Frege held that ideas are ‘privately owned’; as he wittily put it, ‘I can’t have your pain, and you can’t have my sympathy’. But this is mistaken, as Wittgenstein showed. The distinction between numerical and qualitative identity does not apply to ideas, and two people can have exactly the same idea (PI §253; see Exg. and Volume 3, ‘Privacy’, sect. 2). However, recognizing that it is incoherent to suppose that ideas are privately and inalienably owned does not reinstate the possibility of explaining what it is for a word to have a meaning by reference to the thought that the meanings of words are ideas in the mind. Among other things, ideas cannot function as samples (see Volume 3, ‘Private ostensive deﬁnition’), and the meaning of a word is not an entity of any kind, not even of an aethereal kind.

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atomist phase.11 A language must be learnable — it must be possible to teach others what the expressions of one’s language mean. This in turn implies that there must be extensive agreement not only in deﬁnitions (or, more broadly, in explanations of word-meaning) but also in judgements (PI §242), for a learner’s mere mastery of deﬁnitions without broad consensus in judgements with proﬁcient speakers would betoken lack of understanding. Being teachable, the meaning of an expression may be understood, not understood or misunderstood by the learner. So there must be right and wrong ways of understanding what an expression means, as there must be right and wrong ways of using it — i.e. meaning must be construed to be, in this ‘thin’ sense, a normative notion. Whether the notion of normativity involved is to be taken thinly or ‘thickly’, i.e. as involving rule-governed regularity, is a matter of dispute. What cannot be disputed is that Wittgenstein insisted upon this. Inasmuch as we use sentences to describe how things are, what we then say can be evaluated as true or false. But the meanings of the sentences we use to say something truth-evaluable are presupposed by any investigation into the truth or falsity of what was asserted. The principle that meaning is independent of truth may be called the independence requirement. It must, in general, be possible to grasp the meaning of a sentence and what was meant by the utterance of that sentence independently of knowing whether what was said by its use is true or false. Exceptions to this requirement, as in the case of propositions of logic (e.g. ‘Either it is raining or it is not raining’) or of mathematics (‘2 + 2 = 4’), grammatical propositions (e.g. ‘Red is darker than pink’), or propositions of the world-picture (e.g. ‘The world has existed for a long time’), demand a careful investigation of the roles of those sentences (see Volume 2, ‘Grammar and necessity’). Note that the independence requirement is compatible with the consensual requirement that broad agreement in judgements is needed for the possibility of communication by means of language. Word-meaning must, by and large, be indifferent to the discourse function of the sentence in which a word is embedded. In particular, an explanation of the meaning of a word must, in general, be equally serviceable in explaining its meaning in declarative sentences that may be used assertorically, imperatives that may be used to issues orders, and interrogatives that may be used to query. Securing this requirement has proved to be highly controversial relative to the conceptions of meaning that dominated philosophical reﬂection in the twentieth century. In the latter half of the century, the pivotal internal relation that was seized upon by philosophers in the wake of Tarski and Carnap was the relation of meaning not to truth but to truth-conditions. For the meaning of a declarative sentence was held to be given by speciﬁcation of the conditions under which such a sentence (sic) is true. This was interpreted to mean not the conditions that a sentence must satisfy in order to express something 11

He held that logically proper names retain their meaning only ‘for about a minute or two’ (PLAt 180).

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that is the case,12 but rather the circumstances that must obtain for the sentence to be true (hence not a condition on the sentence).13 Word-meaning was then construed in terms of the contribution that a word makes to the determination of the truth-conditions of any sentence in which it may occur. But, as we have seen (‘Descriptions and the uses of sentences’, sects 1–3), this impales the theorist upon the horns of a dilemma. For either he is committed to the analysis of all sentences, including non-assertoric ones, into a truth-valuebearing sentence-radical and mood-operator, or he must hold that words as they occur in non-assertoric sentences have no meaning or a quite different meaning. Wittgenstein showed that the former alternative is incoherent; and the latter is surely absurd. The contextual insight that words contribute to the determination of what is said by means of sentences in which they are embedded is important — they are, as was observed more than 2,000 years ago, parts of speech (see ‘Contextual dicta and contextual principles’). Although it is mistaken to claim that words have a meaning only in the context of a sentence, it is true that one says things by the use of sentences (even if they are one-word sentences), and that the constituent words of a sentence contribute to the determination of what can thereby be said, queried, requested, ordered, etc. Just as a chess piece is put to use in a move, and a move is an actual move (as opposed to an example or rehearsal of a move) only in the context of a game, so too words are put to use (primarily) in the context of utterances or speech-acts, and to be able to perform a speech-act is to have mastered (a signiﬁcant fragment of ) a language. But it would be misleading to claim that the meaning of a sentence is literally a function of the meanings of its constituent words, and even more misleading to suppose that what is said by the use of a sentence is literally a function of the constituent words. The meanings of words are not the arguments of functions the values of which are sentence-meanings or propositions expressed by the use of sentences. It is equally misconceived to suppose that the meaning of a sentence is composed of the meanings of its constituent words, let alone that what is said by the use of a sentence is composed of word-meanings — as if the meanings of words were ingredients of the meanings of sentences or of what is said by their use. 12

This being the conception of a truth-condition characteristic of the Tractatus. So, for example, ‘p and q’ has as its truth-condition that both conjuncts be true, whereas ‘p or q’ satisﬁes the requirements on it if only one disjunct is true. Clearly, the concept of a truth-condition here is a condition that must be met by the molecular proposition. But there is no condition that an elementary proposition ‘p’ has to satisfy in order to be true — things just have to be as it describes them as being. But that things have to be as the proposition describes them as being is not a condition the proposition has to satisfy in order to be true, but a speciﬁcation of what it is for the proposition to be true. 13 This being the conception of a truth-condition derived from Tarski. Furthermore, the error of ascribing truth-values to sentences rather than to what is said by their use is above all due to him.

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What words mean must in general be transparent to their users — we do not wait upon philosophers or scientists to discover what we mean by the words we use and the sentences we utter — and what we mean is, standardly, what they mean — we may call this the transparency requirement. It has been characteristic of philosophers in the early analytic tradition, such as Frege (a precursor of analytic philosophy), Russell and the early Wittgenstein, and the later phases of the analytic tradition (cf. theorists of meaning for a natural language, such as Davidson) to override this requirement. For analysis was assimilated to discovery, and it was analysis that would reveal the real meanings of expressions (e.g. of number-words) for the ﬁrst time. So it was held to be a philosophical discovery of the ﬁrst order (a ‘paradigm of philosophy’, as Ramsey put it) that a sentence of the form ‘The ϕer ψs’ contains two quantiﬁers and an identity-sign in its depth grammar; or, to give a more recent example, that a sentence of the form ‘A V ’d quickly in S at t’ incorporates quantiﬁcation over events, and so contains a quantiﬁer, a verbal noun and conjunctions in its depth grammar (‘There was a V-ing such that it was done by A, and it was quick, and it was in S, and it was at t’). Such paraphrastic possibilities do show something, but the transparency requirement suggests that this cannot be what their proponents had hoped that they show, e.g. the logical structure of the world, the logical form of thought, the depth grammar of a fragment of language (see PI §§60–3). Wittgenstein’s various requirements on any acceptable explanation of our concept of word-meaning (as applied to a developed language) are summarized in the following table. 1. Shareability 2. Objectivity 3. Constancy 4. Regularity 5. Learnability

6. Normativity

7. Truth-independence

‘Private’ languages that no one other than the speaker could in principle understand must be precluded. The possibility of describing how things objectively are must be ensured. Reasonable constancy of meaning over time must be ensured. There must be regularity in the employment of words. It must be intelligible that those who do not know the language can learn it, and that those who do can teach and explain what the words mean. Word-meaning must be construed normatively, minimally in the sense that it be possible to understand or misunderstand a word or sentence and to explain and to use a word correctly or incorrectly (maximally in the sense that explanations of what a word means constitute a rule correlative to a regularity in a practice). In general, it must be possible to understand what is said by a signiﬁcant sentence in use independently of knowing whether it is true; exceptions demand special explanation.

Meaning and use 8. Indifference to sentential discourse function 9. Contributory to a move in a language-game

10. Transparency

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Explanations of word-meaning must hold irrespective of the discourse-function of any sentence in which the word may occur. The concept of word-meaning must be so explained as to do justice to the fact that it is by the use of sentences (including one-word sentences) that a move is made in a language-game, and that the meaning of a word contributes to the determination of what is said by a sentence in use in which it occurs. The meaning of a word must be so construed as to exclude the possibility that it is opaque to proﬁcient speakers.

To some philosophers, some of these requirements will seem controversial. Wittgenstein’s arguments for them will be rehearsed in due course, in various essays of this Commentary. To others, many of them will seem platitudinous. And so, in a sense, they are. What is remarkable is how often great philosophers’ reﬂections on linguistic meaning have failed to satisfy them. The history of reﬂections on linguistic meaning shows philosophers to be subject to divergent pressures. On the one hand, there is a patent subjectivizing pressure, i.e. a pressure to conceive of the meanings of words as essentially mental entities — ‘ideas’ or representations in the mind — and to conceive of the assignment or determination of meaning as a matter of correlating words with ideas. Many factors pertaining to the relation between thought and language, thinking and speaking, and to the putative foundations of knowledge and of language, have tempted philosophers from Aristotle onwards to advance such a view. On the other hand, there is an equally powerful objectivizing pressure, i.e. a pressure to conceive of the meanings of words as something objective and mind-independent. This may involve one or another of two divergent conceptions, one focused on logical relations, the other on intentionality. The ﬁrst moves in a Platonizing direction, conceiving of the meanings of words as abstract entities that stand in determinate logical relations to each other. Here the determination of the meaning of a word is conceived to be a matter of correlating a word with an abstract entity. This conception pays due homage to the objectivity and apparent sempiternality of logical truths and logical relations.14 The second moves in an objective but less abstract direction, conceiving of the meanings of words as items in the objective world with which words, or perhaps only simple indeﬁnable words, are correlated (e.g. the Tractatus). This conception budgets for the intentionality of language, and hence for the representational character of the assertions in a language (see Volume 4, ‘Intentionality’). In the case of the Tractatus picture theory of representation, it was designed to secure the possibility of a 14

‘Apparent’, since atemporality is typically confused with omnitemporality.

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proposition’s being false yet meaningful, or, more speciﬁcally, the possibility of thinking what is not the case. These tendencies in philosophical reﬂection are typically (but not uniformly) exhibited by reﬂections that lie within the force-ﬁeld of the Augustinian conception of meaning, according to which words have meanings, the meaning of a word is something correlated with it, and ostensive deﬁnition (or association) is the original mechanism linking words and the (objective or subjective) world. It is evident that Wittgenstein’s primary target in the Philosophical Investigations is the Augustinian conception of language and its corollaries. He did not deny that some words, sometimes, can be said to stand for something. But he insisted on clarifying what this opaque phrase means — for it does not mean what he had once argued that it means: namely, that the word goes proxy for the object it stands for in the linguistic representation of a possible state of affairs of which that object is a constituent. After all, it is not as if the entity that the word stands for can replace the word in the sentence — ‘the sign on the map is not a substitute for the object it means’ (RPP I, §207). At most, an object pointed at, an ostensive gesture +, and the demonstrative utterance ‘this’ (or ‘this so-and-so’) can conjunctively replace a word (e.g. ‘red’) in a sentence (e.g. ‘The curtains are this + colour (pointing at a sample of red)’ rather than ‘The curtains are red’). And what that shows is that the deﬁniens in an ostensive deﬁnition is a (partly concrete) symbol, not a link between language and reality (see ‘Ostensive deﬁnition and its ramiﬁcations’). To say that a certain word signiﬁes or stands for a certain thing (e.g. that ‘Jack’ signiﬁes or stands for him +, or that ‘scarlet’ signiﬁes or stands for that + colour) may be unobjectionable (PI §10). To say that all words signify or stand for some thing or other is not so much false as vacuous (PI §13). One can say that the word ‘three’ stands for a certain number, that ‘to perambulate’ stands for an activity, that ‘slowly’ stands for a mode of action, and that ‘and’ stands for a binary relation. But that does not make a number-word, a verb, an adverb and a logical connective any more alike in their roles — which are very different. ‘Standing for’ may be too closely tied to the Augustinian conception that words are correlated with objects that are their meanings. But being a word for is a close cousin, and more ﬂexible.15 Appropriately, it does not apply to proper names (‘Napoleon’ is the name of, not a word for, the victor of Austerlitz). It does not demand the existence of the thing that a given word is said to be a word for (e.g. ‘dragon’ is a word for a kind of mythological monster, ‘phlogiston’ a word for a supposed substance once hypothesized to explain combustion). One can say, perfectly correctly, that ‘table’ is the word for such + pieces of furniture, that ‘red’ is the word for this + colour, and that ‘three’ is the word for this + ••• number of things. One might, indeed, invoke the same formula to explain what connectives such as ‘and’, ‘or’ and ‘but’ 15

A suggestion made and exploited by B. Rundle, Wittgenstein and Contemporary Philosophy of Language (Blackwell, Oxford, 1990), ch. 1.

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mean — expressions that do not readily lend themselves to the formula ‘the meaning of “W” is . . .’. ‘And’, one could explain, is a word typically used to indicate that a thematic continuity is to be seen between conjoined sentences. But, of course, that does not mean that it stands for, or even that it is correlated with, a thematic continuity, in the sense in which one might say that ‘red’ stands for, or is correlated with, this + colour. Similarly, ‘perhaps’ might be said to be a word for indicating hesitation or qualiﬁcation, but it is not correlated with a qualiﬁcation, it expresses one. ‘Three’ is a word for a number, but it is not correlated with the number three — it is used for correlating objects with counting up to three. ‘Left’ (or ‘is to the left of ’) signiﬁes, is a word (or phrase) for, a relation, and it can be explained by ostensive deﬁnition — but the sample it is correlated with is not that relation, but rather objects’ standing in that relation. And so on. The ﬂexibility of being a word for is patent, and its proximity to meaning is clear. The moot question is whether explaining ‘the meaning of a word’ in terms of being a word for is illuminating, and, in the context of Wittgenstein’s discussions, whether this sheds light on the matters that he is keen to illuminate. ‘Being the word for’, no less than ‘stands for’, imposes a constant form of representation upon words and the explanations of what they mean. To that extent it is in danger of obscuring the diversity of role and function of words, which Wittgenstein thought was highlighted by associating meaning with use and the diversity of use as exhibited, for example, in the diversity of explanations of use. For one can readily display, as he already did in Investigations §1, how different the uses of what he liked to call ‘different parts of speech’ (kinds of words) are. Indeed, in §1, he in effect operationalizes use by artiﬁcially highlighting the diversity of the uses (modes of application) of sortals, colour-names and number-words. What Wittgenstein does object to (see Exg. §1) is the crude error he had inherited from Frege and Russell, of holding that the meaning of a word is the object it stands for. The thought that the bearer of a name is the meaning of the name exempliﬁes this confusion in its simplest form. It is a misconception. In certain cases one can replace the name ‘A’ by the expression ‘the bearer of the name “A” ’ (e.g. ‘Mr N.N.’ by ‘the bearer of the name “N.N.” ’ or ‘red’ by the expression ‘The colour that bears the name “red” ’).16 But it does not follow, and indeed it is absurd to suppose, that the bearer of the name ‘A’ is the meaning of ‘A’. For if the bearer of the name ‘A’ ceases to 16

As has been noted elsewhere, Wittgenstein surprisingly overlooked the fact that we do not ordinarily speak of proper names of people as having a meaning at all (save in the irrelevant sense in which ‘Peter’ means ‘rock’). Discussion of this matter is deferred until ‘Proper names’ and Exg. §79. It does not affect the argument here. Moreover, neither Russell nor the young Wittgenstein thought that ordinary proper names are, logically speaking, names at all. So their misguided thesis that the meaning of a real name (a logically proper name) is the object it stands for was never intended to apply to ordinary proper names, but only to names of ‘particulars’ or ‘simple objects’ (see ‘Logically proper names’, sects 1f.).

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exist, it does not follow that the name ceases to have a meaning (PI §40). It is patent that the very idea that the meaning (Bedeutung) of a word might be the entity the word can be said to stand for was predicated upon a misconstrual of the concept of meaning. The meanings of words are not objects or entities of any kind. This is why Wittgenstein remarked in 1931 that the concept of meaning is now obsolete save for such expressions as ‘means the same as’ or ‘has no meaning’ (M 52; AWL 30). We may be confused, in the simple case, by the fact that we often explain what a name means by pointing at something and saying ‘That + is A’ (PI §43). However, we are not pointing at the meaning of A, but at A (or a sample of A).17 There is no question but that the simple procedure of ostensive deﬁnition is (philosophically) confusing. For not only may it incline one to think that what one is pointing at is the meaning of the word, but it also encourages a deeper confusion. We readily suppose that in order to be able to symbolize how things are in the world, language must be connected to reality. And if one thinks thus, it is very tempting to construe ostensive deﬁnitions as ﬁxing the points of connection. Then one may be disposed to think that language consists of deﬁnables and indeﬁnables, the former constituting the web of words, the latter constituting the nodes where the web is pinned to the world (NB 53), and so too the point at which content is, as it were, injected into the network of language. But, as Wittgenstein clariﬁed, samples employed in an ostensive deﬁnition belong to the means of representation, and ostensive deﬁnition remains within language. It is a rule for the use of the word deﬁned, not the point at which we exit from language (see ‘Ostensive deﬁnition and its ramiﬁcations’, sect. 3). If the meanings of words are not entities of any kind, then a fortiori they are not ideas in the mind, abstract entities, or ‘objects’ that are part of the substance of the world (TLP 2.02ff.). But to dispel the powerful illusions that have inclined great thinkers to suppose otherwise, one needs to do a great deal more than point this out. For one must dig down to the roots of the error. This Wittgenstein did in his criticisms of the logical and ontological confusions of the Tractatus (see ‘Logically proper names’, sects 3f., and ‘Ostensive deﬁnition and its ramiﬁcations’, sect. 6), in his account of necessary truths and criticisms of Platonism (see Volume 2, ‘Grammar and necessity’) and in his private language arguments (see Volume 3, ‘Private ostensive deﬁnition’).

3. Wittgenstein: meaning and its internal relations Having rejected the conception of meaning that he had taken over from his predecessors and reﬁned in the Tractatus, Wittgenstein linked the concept of 17

For present purposes, we may disregard the fact that in §43 Wittgenstein is thinking of ‘A’ as a proper name, and misguidedly ascribes it a meaning.

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meaning with a number of closely associated concepts. First and foremost, he connected the meaning of a word with its use (PG 60). For a large class of cases (PI §43), we can explain the phrase ‘the meaning of a word’ as having the same meaning as ‘the use of a word in the language’. In his lectures he remarked ‘I have suggested substituting for “meaning of a word”, “use of a word”, because use of a word comprises a large part of what is meant by “the meaning of a word” ’ (AWL 48).18 The reasons for the qualiﬁcation will be examined in section 4 below. Wittgenstein raised the question of whether the meaning of a word is really only the use of the word. Is it not the way this use meshes with our life (PG 65)? To be sure, one cannot cash the phrase ‘the meaning of a word’ by the phrase ‘the way the use of a word meshes with our life’. And Wittgenstein responds to his own query with the reply: ‘But isn’t its use part of our life?’ By contrast with his conception of language in the Tractatus, he was now eager to emphasize the manifold ways in which the use of words is integrated in human life and action. Words, he remarked, are deeds. To speak is to do something. The uses of words are woven into the tapestry of human life. Indeed, our ability to master the use of words and the uses we thus master are partly constitutive of our nature. We are what we are and can do those things that characterize us as human beings, because we are language-users. For it is our mastery of the techniques of the uses of words that determines the horizon of our possible beliefs and of our will, endows us with our capacity for selfconsciousness, makes it possible for us to engage in reasoning from given premisses to a conclusion, and to act for reasons. The use of a word, Wittgenstein averred, is determined by the rules for the use of that word (AWL 30). For using words in speech is a rule-governed activity. The rules for the use of a word are constitutive of what Wittgenstein called ‘its grammar’. He used the expression ‘grammar’ in an idiosyncratic way (see Volume 2, ‘Rules and grammar’, sects 4 –5) to refer to all the rules that determine the use of a word, i.e. both rules of grammar acknowledged by linguists and also what linguists call ‘the lexicon’ and exclude from grammar — i.e. the explanations of meaning (LWL 46f.). To grammar belongs everything that determines sense, everything that has to be settled antecedently to questions about truth. The grammar of an expression, in Wittgenstein’s generous use of ‘grammar’, also speciﬁes the licit combinatorial possibilities of the expression, ‘i.e. which combinations make sense and which don’t, which are allowed and which

18

He acknowledged that the use of a word seems to be internal to the language-game with it, but that the meaning appears to point to something outside the game (presumably to the thing the word is a word for). That, Wittgenstein observes, suggests that ‘meaning’ and ‘use’ are ‘not equatable’; but ‘this is misleading’ (AWL 48, emphasis added). Why is it misleading? Presumably because it inclines us to think that to have a meaning is to stand for something, that the meanings of words are the items in the world with which words are correlated, that language is, in a misleading sense, connected to reality.

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are not allowed’ (ibid.; emphasis added).19 ‘What interests us in the sign’, he wrote, ‘the meaning which matters for us, is what is embodied in the grammar of the sign. . . . Grammar is the account books of language’ (PG 87). Wittgenstein contended that the questions ‘How is the word used?’ and ‘What is the grammar of the word?’ are one and the same question (ibid.). The use of a word is what is deﬁned by the rules for its use, just as the use of the king in chess is deﬁned by the rules (AWL 48). The meaning of a sign lies in the rules according to which it is applied, in the rules that prescribe its use (MS 114 (Vol. X), 4r). Two words have the same meaning, he said, if they have the same rules for their use (AWL 3).20 Wittgenstein’s observations on the meaning, use and rules for the use of words place him ﬁrmly on the side of ‘thick’ interpretations of the normativity of language (but, as we shall see below, his position stands in less stark a contrast with the ‘thin’ interpretation than may appear, since his conception of rules is relaxed and elastic). Among the rules for the use of a word are explanations of meaning, i.e. answers to the question ‘What does “W” mean?’, or ‘What is the meaning of “W”?’, or even just ‘What is (a) W?’. The meaning of a word is what is given by an explanation of meaning, and an explanation of what a word means is a rule for the use of the word explained. ‘An explanation of meaning is not an empirical proposition, not a causal explanation, but a rule, a convention’ (PG 68). The explanation of the meaning of a word explains the use of the word (PG 59). Bearing in mind his own earlier confusions, and those of Frege and Russell, Wittgenstein remarked that explanations of meaning are, as it were, ‘concrete’, and are less likely to lead us to chase shadows in the way the confusing word ‘meaning’ does (MS 116 (Vol. XII), 32). It is noteworthy that the Blue Book opens by suggesting that the question ‘What is the meaning of a word?’ should be dealt with by examining what an explanation of the meaning 19

Hence not conversational conventions (or ‘implicatures’). That we would not say something because it is too obvious is not, as Wittgenstein used the terms ‘grammar’, ‘use’, ‘explanation of meaning’ and ‘rules of use’, part of the grammar, use or meaning of an expression, and is not incorporated into explanations of meaning. It is true that we would not answer the question ‘What are you doing?’ by saying ‘I am reading a book and breathing’, even though it is true that I am breathing. It is also true that we would not normally answer the question ‘What did you say?’ by ‘I tried to say “Yes” and I did say “Yes” ’, but that is not because it is true that I tried but that it is too obvious to be worth saying that I did. It is rather because it is not true that one tries to do whatever one voluntarily does (for discussion, see Volume 4, ‘Willing and the nature voluntary action’, sect. 6(b)). Whatever truth there is in Gricean implicature does not show that the meaning of a word is not its use or not given by specifying the rules for its use. For the rules for the use of a word, as given by explanations of meaning, determine what makes sense, not what is or is not worth saying. One would not normally say that one is breathing, but it makes sense to say it. One would not normally say that one tried to do something that one effortlessly does, and if one did, one would not be understood. 20 However, as we shall see below, the fact that words are used according to somewhat different rules does not necessarily imply that they have a different meaning or that their meaning differs in all contexts. That depends on a further distinction between what is essential and what inessential, which is often a context-dependent matter.

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of a word is. This, again, ‘operationalizes’ the question, and is analogous to replacing the question ‘What is length?’ by the question ‘How do we measure length?’ (BB 1). As noted (see ‘Explanation’, pp. 33f.), he observed that the grammatical platitude that meaning is what is given by an explanation of meaning could be interpreted thus: ‘Let’s only bother about what’s called the explanation of meaning, and let’s not bother about meaning in any other sense’ (PG 69). For then we shall not be tempted to reify meanings, or to think of the meanings of words as something that is correlated with the word (cf. BB 1), any more than we are tempted to think of the use of the chess king, which is explained by specifying the rules according to which it can be moved, as being something that is correlated with the king. Since the rules for the use of a word are themselves part of the totality of rules of the grammar of the language, one can also say that the meaning of a word is its place in grammar. For the rules for the use of any given word determine which ‘part of speech’ it is, what combinatorial possibilities it admits of, what are the grounds for its application. They interlock in a variety of ways with the rules for the use of other words. For it is rules of grammar that determine compatibilities, incompatibilities, implications and mutual implications of such-and-such a predication with other propositions. Wittgenstein had earlier expressed this by observing that the meaning of a word is its place in the calculus (PG 63). As he gradually distanced himself from the calculus conception of language, he replaced that observation with the former principle. Grammar, he insisted, describes the use of words in the language (PG 60). This is a misleading formulation, since it suggests that grammar is part of the natural history of language. That this is not what Wittgenstein meant is evident from his next remark in the very same passage: ‘So it has somewhat the same relation to the language as the description of a game, the rules of a game, have to the game’ (ibid.). The sense in which the rules of chess describe the game of chess is that they specify how the game is to be played.21 That is not part of natural history — for natural history would have to include all the misuses and misapplications of rules (cf. MS 110 (Vol. V ), 65). It is a normative description — like the description of a legal system.22 To be precise, grammar (in Wittgenstein’s extended sense) states, rather than describes, the rules of language. The meaning of a word is given by explanations of meaning. Explanations of meaning are rules for the use of the explanandum. These grammatical rules determine the meaning of the expression (PG 184). So, pace Frege (BLA ii §136), they themselves are not answerable to any meaning. For grammar is not accountable to any reality, and the rules of grammar constitute the meanings of expressions (M 52) (see Volume 2, ‘Grammar and necessity’, sect. 5, and 21

Of course, how the game is to be played and how it is played converge, and so too do the way a word is to be used and the way it is used. For there has to be ‘agreement in deﬁnitions’ for there to be ‘agreement in judgements’ (cf. PI §242). 22 Of course, that a given culture uses such-and-such expressions according to such-and-such rules at a given time is a matter of history — not natural, but social, history.

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Volume 4, ‘The arbitrariness of grammar and the bounds of sense’, sect. 4), although, of course, that does not mean that the meaning of a word is a list of rules (M 52). It was a mistake of philosophers from Plato to Frege and beyond to take deﬁnition in terms of necessary and sufﬁcient conditions of application to be the paradigm for explanations of word-meaning. Rather, we must recognize the diversity of the forms of such explanations and the ﬂuidity of the various forms. What certain expressions mean is indeed explained by specifying necessary and sufﬁcient conditions of application. But these are the exception rather than the rule. We must also recognize the legitimacy of ostensive deﬁnition (a form of explanation that has no sharp boundaries (see ‘Ostensive deﬁnition and its ramiﬁcations’, sect. 2)), of explanation of familyresemblance concepts by a series of examples together with a similarity-rider (see ‘Family resemblance’, sect. 3), of explanation by paraphrase and contrastive paraphrase, of explanation by citing grounds of application, criteria that warrant application (see Volume 3, ‘Criteria’, sects 2f.), verifying conditions of a predication, and so forth (see ‘Explanation’, sect. 3). A further node in the network surrounding the concept of meaning is that of understanding. For the meaning of a word is an object of understanding. It is what is understood or known when one has mastered the technique of the use of that word. So too, the meaning of a sentence and what is meant by its use on an occasion of utterance are what is understood when a hearer understands the utterance. There are three kinds of criteria of understanding. A person satisﬁes the criteria for understanding a word if (i) he uses the word correctly, i.e. in accordance with the rules for its use or the received explanation of what it means; (ii) if he correctly explains what the word means; and (iii) if he responds with understanding to the use of the word in question, i.e. responds appropriately or intelligently to utterances in which it occurs. What this latter amounts to is that we can take him to have as part of his reason for responding as he does (including his saying and doing nothing at all) the fact that such-and-such was said. We can summarize that part of the web of words surrounding the concept of the meaning of a word that Wittgenstein highlighted in a ﬁgure, the vertical axis of which reaches up from normativity to practice. place of a word in life use of a word

explanation of what a word means

meaning of a word

rule for the use of a word place of the word in grammar

understanding a word, knowing what it means

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It is evident that by emphasizing the conceptual connection between meaning and use, Wittgenstein reduces the temptation to conceive of the meaning of a word as an entity of any kind, no matter whether concrete or abstract, particular or universal, that is correlated with the word. He also undermines the ideas that a word’s having a meaning is a matter of its being correlated with something extra-linguistic, and that understanding a word or knowing what it means is grasping such a correlation. And he undercuts the thought that the web of language is given meaning by connections with reality (and to that extent, parts company with received conceptions of semantics). But the shift of focus also effects a further beneﬁt. It sheds light on the relation between conventional, linguistic meaning and what is meant by the use of an expression — a matter to which we shall now turn. It is tempting to say that words and sentences are, in themselves, mere sounds or marks on paper. They are arbitrary. The sounds that are used in one language to mean something may be quite different from the sounds used in another language. And we may be tempted to say that although ‘black’, ‘schwarz’ and ‘noir’ are altogether different sounds or marks, English, German and French speakers ‘attach the same meaning’ to them. What meaning is ‘associated’ with a given mark or sound is an altogether conventional matter. So it is natural to suppose that words can stand for things, and that sentences can represent (truly or falsely) how things are only in virtue of the associative or intentional activities or experiences of the speaker who uses them and of the associative or interpretative activities or experiences of the hearer who hears and understands them. Without these, the signs would be dead. What gives them ‘life’ are surely the mental acts, activities and experiences of language-users (cf. BB 3). A mere inscription, in and of itself, says nothing, signiﬁes nothing, stands for nothing. For a word to signify the entity it stands for, we may be inclined to reason, for a name to signify its bearer, for a predicate to be the word for the property of which it is the name, it must surely be meant by the speaker as a sign for whatever it represents — must be intended to signify that thing. Intention, it seems, is the method of projection (MS 108 (Vol. IV), 219; cf. MS 145, 49, quoted in note to Exg. §95). Pari passu, what makes the mere sounds that a speaker hears into meaningful discourse signifying whatever it signiﬁes, is the hearer’s activity of interpreting the sounds as signs for things (or, on classical empiricist conceptions, the experiences of the hearer, who associates the sounds heard with ideas in his own mind). Once the construction lines between the meaning of an expression and its grammatically determined use, and between the meaning of an expression and the explanations of what it means, conceived as rules for its use, are drawn, these temptations become easier to resist. For meaning something by a word is not an act or activity of any kind — one cannot ask how one does it, or how long it takes, whether it is easy or difﬁcult, whether one has succeeded or failed to mean something, or whether one has ﬁnished meaning something (see Volume 4, ‘The mythology of meaning’). It is perfectly correct to think

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that when one uses a word, one means something by it, and means something by the sentence incorporating it, which one utters. But to mean something by a sign is not to do anything — it is not a special mental act, activity or process that gives ‘life’ to a sign. ‘If we had to name anything which is the life of signs, we should have to say that it was its use’ (BB 4). Moreover, it is the fact that words have an established use that makes it possible for speakers to mean things by them and by the utterance of sentences in which they occur, and also constrains what a speaker can mean by them (PI §§507–14).23 One does not, of course, attach meanings to words (meanings are not attachments) or even associate meanings with words (words are not Rorschach spots for their meanings). Rather, one uses words in accordance with the rules for their use, rules which are constituted by explanations of meaning (explanations which are typically given by another word or words). The use of a word is not akin to an entity, and that a word has a certain rule-governed use is not something that we could conceivably ‘attach’ to words, any more than the use of a tool could be ‘attached’ to it. Not only is it not the speaker’s meaning (intending) whatever he means by his words, that gives the signs he uses their meaning, it is likewise not the hearer’s interpretation that renders the sounds he hears signiﬁcant or enables him to understand them. Understanding is not, in general, a matter of interpreting, and the signs heard or read are not endowed with meaning, either objectively or subjectively, by acts of interpreting. On the contrary, interpreting presupposes both meaning and understanding. For an interpretation is called for only where an utterance admits of alternative meanings in its context, and one is called upon to choose between them. Moreover, what is heard are not merely sounds impacting upon one’s ear-drums, and what is read are not merely inscriptions (marks on paper), but signiﬁcant words of one’s language — and they are unavoidably heard and seen as such. Normally, one does not interpret what one hears; one understands what is said to one without any interpretation (PG 39f., 45–7; BT 2f., 16f., 20; PI §§201, 433, 503–6). The shift of focus to the grammatically determined use of words also satisﬁes the desiderata for any cogent account of meaning. Unless there can be ‘private’ rules for the use of an expression, i.e. rules that no one other than the speaker can understand and follow, the (qualiﬁed) identiﬁcation of meaning with use satisﬁes the sharability and communicability requirements. Wittgenstein’s ‘private language arguments’ show that the idea of ‘private’ rules (and hence ‘private’ meanings) is incoherent. So there is no barrier to different people’s knowing the rules for the use of an expression, or to their using the expression in accordance with common, and commonly understood, rules. Rules for the use of words, constituted by explanations of what the words 23

That is why attempts to reduce linguistic meaning to speakers’ communication intentions (cf. Grice’s account of meaning) are doomed to failure, for the sophisticated intentions that need to be invoked are themselves dependent upon the speaker’s mastery of a language.

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mean, are eminently teachable and learnable. Taking what words mean to be speciﬁed by rules for their use, the concept of meaning is construed normatively, and normativity is taken ‘thickly’. (On the other hand, the concept of a rule is taken in a ﬂexible and relaxed manner. The concept of a rule, Wittgenstein held, is a family-resemblance concept. There are many different kinds of rule (the variety often being overlooked or disregarded by philosophers and linguists). So he emphasized that a series of examples in a familyresemblance explanation constitutes a rule; he characterized an ostensive deﬁnition as a rule, for it functions as a standard of correct use for the deﬁniendum; he treated signposts, charts or tables as forms of rules.) Linking meaning to use and explanation of meaning to rules of use satisﬁes the constancy and regularity requirements, since, as Wittgenstein laboured to clarify in his discussions of following a rule, a rule is internally related to a practice (see Volume 2, ‘Following rules, mastery of techniques and practices’). Conceiving of the meaning of a word as what is given by an explanation of its meaning distances us from idealist conceptions of meaning that fail to meet the objectivity requirement. For we do not explain what words mean by referring the learner or questioner to ideas in his mind. Moreover, it also distances us from truth-conditional theories of meaning that require a distinction, in every sentence, between a force-operator and a truth-value-bearing sentence-radical, in order to budget for the occurrence of words in imperative and interrogative sentences that prima facie have no truth-conditions. For humdrum explanations of meaning are equally valid for what the words mean in imperative and interrogative sentences that do not express propositions (bearers of truthvalues) as they are for explaining what those words mean in declarative sentences. The independence of meaning from truth is a requirement on a wide but not exhaustive range of propositions. Those propositions that patently do not satisfy it, such as propositions of logic, mathematics, grammatical propositions (including analytic propositions) and propositions of the world-picture are extensively discussed by Wittgenstein. Logical truths, he continued to think, are degenerate, limiting cases of propositions. They say nothing, but they are systematically related to rules of inference. As far as his treatment of mathematical and grammatical propositions is concerned, it is striking that far from trying to explain the source of their necessity and the manner in which we come to recognize them, he pressed the question of their role and function. They are rules, not descriptions of mathematical reality or of metaphysical necessity. Arithmetic is essentially a system of rules for the transformation of empirical propositions about quantities, dimensions, etc. of things. Grammatical propositions are rules for the use of their constituent words in the misleading guise of descriptions of necessities in the world. In short, the focus upon the uses of expressions provided part of the inspiration for a resolution of the most fundamental philosophical problems concerning the nature of necessary truths (see Volume 2, ‘Grammar and necessity’). The transparency requirement is met by relaxing the demands on explanation of meaning. We do not wait on the

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activities of philosophical analysts to reveal to us for the ﬁrst time what the words we use mean.24 Since one criterion of understanding is giving an appropriate explanation in context,25 it makes little sense to suppose that a person might use a word with understanding and be unable to say what he meant by it, or, minimally, to recognize a correct explanation if offered one.26 And if what he meant by it does not coincide with what it generally means in accepted usage, then either he was using it in an extended or novel sense (which he must surely be able to explain), or he did not know what he was saying.

4. Qualiﬁcations For a large class of cases, Wittgenstein averred, the meaning of a word is its use in the language. This is not a theory or hypothesis, but a grammatical remark. It is important to remember Wittgenstein’s qualiﬁcations: ‘for a large class of cases’ — and: that ‘use of a word’ comprises a large part of what is meant by ‘the meaning of a word’. What qualiﬁcations did he have in mind? Presumably he was thinking of contexts in which ‘meaning (of a word)’ and ‘use (of a word)’ are not interchangeable (see Exg. §43). This is exempliﬁed by some of his own idiosyncratic uses. He speaks of ‘meaning-blindness’, but not of ‘use-blindness’, of ‘experiencing the meaning of a word’, but not of ‘experiencing the use of a word’, and ‘meaning’ and ‘use’ are not here interchangeable, as he surely must have noticed. Similarly, he invokes the metaphor of a meaningbody, but one could not speak of a use-body. So ‘meaning’, even in contexts in which it is the meaning of a word that is at issue, does not always mean the same as ‘use’ (of a word). That does not imply that they never have the same meaning. (It is evident from other remarks that Wittgenstein was not committed to the view that synonymy is context-independent and an all-ornothing affair.) But, as we shall see in a moment, he was also aware of other divergences than these (see Exg. §§547–70). 24

We did not need Frege to tell us that ‘one’ means ‘the number which belongs to the concept “identical with 0” ’ (FA §77), for, ingenious though this deﬁnition is, it is not how we explain what the number word ‘one’ means; nor would it provide anyone in need with a standard of correct use for that number-word. And we certainly did not need Frege to tell us that ‘nought’ means ‘the number which belongs to the concept “not identical with itself ” ’, since there is no such concept (there is no such thing as not being identical with oneself; hence too, no such thing as being identical with oneself either (see Exg. §216)). 25 Of course, a child acquires rudimentary mastery of the use of a word ‘W’ before he can answer the question ‘What does “W” mean?’ and before he can even ask ‘What is the meaning of “W”?’. To just that extent, then, his understanding is rudimentary, and his ability to move around freely in the web of words is limited. 26 ‘Yes, of course’, one might say when another offers one an explanation of a word, the use of which one has mastered, and for the explanation of which one is fumbling. But one would not say, ‘Goodness me, is that what it really means? I didn’t know that’ (for then one would not have mastered its use), let alone ‘Heavens! Is that what I meant by it? I didn’t realize that’ (for there is no such thing as meaning something inadvertently).

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In fact, there are many uses of ‘use of a word’ which are not synonymous with ‘meaning of a word’.27 One expression may be used in one place (e.g. ‘a lift’ in Britain) and another in another place (‘an elevator’ in the USA), but they are patently synonymous. One expression (e.g. ‘policeman’, or ‘wireless’) may be used by speakers of one social class or age-group, and another (e.g. ‘copper’, or ‘radio’) by speakers of a different class or age, but they mean the same. One expression may be likely to be used by experts (‘infarct’), and another by laymen (‘heart attack’), but they have the same meaning. A use may be ungrammatical, whereas a meaning cannot be either grammatical or ungrammatical. So too, one may say that the use of a certain word in a given context is tactless, uncalled for, forbidden, frowned on by purists, or likely to provoke a ﬁght — none of which can be said of the meaning of the word. One may say that the use of a certain word is popular among journalists, yet one cannot say that its meaning is popular among journalists. So the phrases ‘the use of a word’ and ‘the meaning of a word’ are not used in the same way. Does this not show that Wittgenstein was mistaken to equate them (even with qualiﬁcation)? Thus far, such a conclusion would be precipitate. The fact that ‘a lift’ is used in one sociolect and ‘an elevator’ in another does not imply that they are differently used in the sense relevant to our inquiry. They mean the same and are used in exactly the same way. It is not obvious that one would want to say that ‘policeman’ and ‘copper’ are used differently, even though one is a vulgarism and the other not. And ‘infarct’ and ‘heart attack’ are surely used in the same way. So too, it is evident that the concept of use that is roughly equated with meaning does not stretch to incorporate ungrammatical uses. But that is because Wittgenstein’s reference to the use of a word, as we have seen, is intended to select something normative. It is use that accords with what is regarded as correct explanation. Similarly, while it is true that a use of a word on a given occasion may be tactless, inappropriate or inept, it is evident that one is here speaking of someone’s making use of the word — tactlessly, inappropriately or ineptly. Finally, while the use of a word may be popular among journalists, whereas its meaning cannot be, all this means is that they like to use it. None of these uses of ‘use of a word’ show that Wittgenstein’s qualiﬁed identiﬁcation of meaning and use is mistaken. Caution is necessary and distinctions need to be drawn. So, if these uses of ‘use of a word’ are excluded, what is Wittgenstein’s conception of use of a word that is in play? Evidently it is the use as determined by grammar (in Wittgenstein’s sense of the term ‘grammar’). And that is the use as given by explanations of how the word is to be used. So we are dealing with a normative (rule-governed) notion. Indeed, perhaps the concept of usage would be less misleading here than use (for while there are misuses, there are no 27

I am indebted for the following considerations to Bede Rundle’s ‘Meaning and Understanding’, in Wittgenstein: A Critical Reader, ed. H. J. Glock (Blackwell, Oxford, 2001), pp. 94–118; see also his Wittgenstein and Contemporary Philosophy of Language (Blackwell, Oxford, 1990), ch. 1.

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misusages). Usage, as spelled out in an explanation of meaning, constitutes a standard of correct use. And Wittgenstein’s conception of use in his equation of meaning and use is patently standard-setting. ‘Copper’ is a vulgarism, and ‘policeman’ is not, but they are used and explained in the same way. If one person said ‘Ask the copper’ and another ‘Ask the policemen’, we would explain what the speakers meant in the same way. The same applies to technical and non-technical expressions: if someone wanted to know what ‘infarct’ means, we should explain that it means the same as ‘heart attack’. The notion of use invoked in Wittgenstein’s qualiﬁed equation of meaning and use is linked with that of an object of understanding. The use of a word is what is mastered when one learns how the word is to be used, when one grasps the technique of its application. So, the moot question is whether, even within these limits, meaning is (with qualiﬁcation) the same as use, or is use the wider, or even a different, notion? Wittgenstein observed that ‘meaning’ is a primitive concept (LW I, §332). And that is surely correct — it is not a sophisticated technical term for linguistic theorists, but an unsophisticated non-technical term for languagelearners who do not understand an utterance or word. The form ‘What does “W” mean?’ belongs to it. So too do the forms ‘ “W” means a V that is F’ and ‘ “W” means the same as “V” ’. But when the concept is expanded to include other words that do not ﬁt into such standard forms, strains are manifest, and difﬁculties and indeterminacies emerge. Unless merely requests for translations into another language, most English speakers feel uncomfortable with such questions as ‘What is the meaning of “if ” (“but”, “and”, “although”) or ‘What does “to” (“on”, “in”, “for”) mean?’. So too, the question ‘What does “perhaps” (“moreover”, “indeed”, “yet”) mean?’ does not invite the answer ‘The meaning of “. . .” is . . .’ or ‘It means . . .’, and not always ‘It means the same as “. . .” ’ either (although that usually is an option if a translation is in question). But one would naturally respond by describing the use of such words. Does this show that meaning and use drift apart? Do these words have a use but no meaning? On the contrary — describing their use is answering, not rejecting, the question ‘What does “. . .” mean?’. After all, one would not answer ‘It means nothing; but it is used thus . . .’. What should be said of words such as ‘Abracadabra’, ‘Tallyho’ or ‘Lillibullero’, or of such jingles in nursery rhymes and fairy-tales as ‘Fee-ﬁ-fo-fum’ and ‘Heydiddle-diddle’? Do they not have a use? And, pace Wittgenstein, proper names of people in our culture surely have uses, but do not have a meaning.28 Do 28 This case will not be discussed here (but see ‘Proper names’). Ordinary proper (personal) names have no meaning (save in the sense in which ‘Peter’ means ‘rock’). To be sure, they have a use (or, indeed, many uses: to name, to introduce, to address, to call, to refer to, etc.). But the concept of use requires scrutiny here. What counts as ‘the use’ of a proper name? Do all proper names have the same use(s)? Or do different proper names (‘John Doe’ and ‘Richard Roe’) have different uses? ‘John Smith’ has thousands of bearers; does it have as many uses as bearers? Is the notion of use here the same as when we speak of the use of the word ‘horse’, ‘red’, ‘three’? Surely further distinctions need to be drawn — if any problems arise.

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these examples not show that the concept of the use of a word is much wider than that of the meaning of a word, and hence that meaning and use cannot be equated? They show that there are differences between the use of ‘the meaning of a word’ and the use of ‘the use of a word’, even within the limitations speciﬁed above. They also suggest differences between having a meaning, meaning the same as, and having meaning (as opposed to being meaningless). ‘Tallyho’ does not readily lend itself to explanation in the form of ‘ “Tallyho” means . . .’, and one cannot say that the meaning of ‘Tallyho’ is. . . . One would indeed explain how ‘Tallyho’ is used by foxhunters: namely, as a cry to indicate that a fox has been sighted. Does this mean that it has a use but no meaning? That would be too swift. For one would be loath to say that it is meaningless. We might say that it has meaning but not a meaning. One would be similarly disinclined to explain the use of ‘Abracadabra’ by saying ‘It means . . .’, although one might say that it means the same as, is used in the same way as, ‘Simsalabim’ in Swedish: namely, when pretending to cast a spell. Like ‘Hello’ or ‘Cheers’ (‘Skoal’), such expressions are not meaningless. Unlike ‘Lillibullero’ or ‘Fee-ﬁ-fo-fum’ (which are not parts of speech), they do have a rule-governed use and are not invoked merely for the sake of the jingle. But they do show the concepts of the meaning of a word and of having a meaning faltering, while that of the use of a word still holds ﬁrm. One may concede that numerous parts of speech (e.g. prepositions, indexicals, connectives, pro-forms, adverbials) sit uneasily with some of the forms of explanation that characterize having a meaning. There are stresses and emergent difﬁculties if the explanation of how such words are to be used is squeezed into forms appropriate for other parts of speech that lend themselves to ‘the meaning of “W” is . . .’, ‘ “W” means . . .’, or to ostensive explanation. But we should not say that these words lack meaning, let alone that they are meaningless. There are aspects of the rule-governed use of words and of the technique of their employment which are not constitutive of their meaning. Wittgenstein noted that we should not want to say that ‘walk’ has a different meaning from ‘walks’ (LW I, §274), and in most contexts in which the question might arise, that is surely right. We should naturally explain what the two forms of the verb mean in the same way — morphology, we might say, is not part of the lexicon (patent in the case of mere grammatical gender in most languages). Nevertheless, ‘walk’ is not used in the same way as ‘walks’, the latter being apt only in the third-person singular. This is part of the grammar of the word, of its rule-governed use. We might say that this difference in use is inessential, that it would not matter to the meaning of the word if this morphological feature were different. So too, one might note that it is a feature of the rulegoverned use of ‘however’ that, unlike ‘but’, it can occur parenthetically. But this does not determine any difference in meaning between the two expressions (by contrast with the use of ‘but’ to mean ‘only’, as in ‘but a triﬂe’).

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Wittgenstein himself observes that ‘not every use . . . is a meaning’ (LW I, §289): if a separate word were used of a tool on each day of the week, it is unclear whether to say that these words all have the same meaning or whether to say that there are seven distinct meanings. He notes that there may be differences in use that are not tantamount to differences in meaning — it all depends whether the difference is essential or non-essential (PI §§561–8; LW I, §385, cf. §326), and that is often a context-dependent and purpose-relative matter. Two words in an imaginary language, ‘non’ and ‘ne’, may be used in exactly the same way, save that reiteration of ‘non’ is an afﬁrmation, whereas reiteration of ‘ne’ is a strengthened negation; so does ‘non-p’ mean the same as ‘ne-p’? Does ‘non’ in ‘non-p’ mean the same as ‘ne’ in ‘ne-p’? One can answer these questions in various ways (PI §556; see Exg.). ‘Why do you ask?’ — is perhaps what one should say in such cases — ‘What is at stake?’ The concept of meaning has ragged edges. Our criteria for sameness and difference of meaning are often indeterminate. If one has to give a determinate answer to this kind of question in a given context, it is a decision that is called for, not a discovery. One must beware, in discussions of synonymy, of thinking of the meaning of a word as anything other than (some aspect or aspects of ) its use, as if one could argue that ‘non-p’ has a different meaning from ‘ne-p’ because ‘non’ has a different meaning from ‘ne’. That would be to succumb to the mythology of compositionalism — as if the meaning of a sentence were composed of the meanings of its sub-sentential constituents, and as if the meaning of a word were something the word carried around with it. Does ‘two’ qua count-number (Anzahl ) mean the same as ‘two’ qua measure-number (Masszahl )? One would be inclined to deny that: there could be 2 soldiers every 2.4 metres, but not 2.4 soldiers every 2 metres. But does ‘two’ in each of its occurrences in ‘There are two soldiers every two metres’ have a different meaning? That one would surely wish to deny (PI §§552f., see Exg.; LW I, §§332–7). Moreover, the concept of identity and difference of use is not sharply determined either. Waismann noted that there is no clear answer to the question of whether someone who uses a hammer ﬁrst to shape glowing iron and then to knock a nail into the wall has used the hammer in one way or in two; similarly, it is often unclear what to count as one use and what as two different uses of a word (PLP 190). Sometimes the matter may be determined by a decision rather than by adducing further features of usage. Such a decision may be guided by considerations of what is essential and what is inessential, or by reference to the purpose of the word (see Exg. §§547–70). So the phrase ‘the meaning of a word’ is not everywhere replaceable by the phrase ‘the use of a word’. There are differences between them. The manifold ramiﬁcations of the concept of the use of a word differ from those of the concept of the meaning of a word. But for many purposes, and in many philosophical contexts, the question of what a given word means and the question of how it is used amount to the same. And if an investigation of the

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meaning of an expression is called for, the way to conduct it is by examining its familiar use. Every difference in meaning is a difference in use; but not every difference in use is a difference in meaning. Can one say that the use determines the meaning? Wittgenstein did query whether it is not the use or application (PI §139; see Exg.) that determines the meaning, but this is in a context where he is probing the relationship between what we grasp at a stroke and the application of a word that is ‘spread out over time’.29 He repeats the point in Investigations §197, but, again, in a context in which he is investigating the puzzle concerning the instantaneous grasping of a rule of a series and its subsequent application in expanding the series. It is not at all obvious that he would countenance saying that the use determines the meaning. True, he urges us to let the use teach us the meaning (PI p. 212/181), but this is in order to encourage us to draw distinctions that we do not ordinarily draw — and how else should we note differences in meaning other than by closely examining differences in rule-governed use. In his lectures he emphasized (rather clumsily perhaps) that a different use is a different meaning (LFM 192, cf. 81f.) — that it would be misleading to suggest that the different meaning follows from or is a consequence of the relevantly different use. The relevantly different use is a difference of meaning — it does not yield a difference of meaning. So, we may grant that not all the rules for the use of an expression are relevant to the meaning of an expression. Nevertheless, the meaning of an expression is not anything other than its use as ﬁxed by the relevant explanations of how the word is to be used (but what is relevant depends on our purposes and interests). For these are constitutive of the meaning. The meaning of a word is not a consequence of the rules for its use as expressed in explanations; it is not something afﬁxed to a word, that the word carries with it from one context to another (MS 116 (Vol. XII), 87f.). One might say that the concept of word-meaning and the concept of the use of a word run, for a signiﬁcant part of their use, along the same track. That they also separate in various places does not mean that their partial coincidence is not of the ﬁrst importance for philosophical purposes of clarifying the hosts of confusions surrounding the concept of meaning. Can one delimit the concept of use to obtain the precise limits of the concept of meaning? On this Wittgenstein had relatively little systematic to say, apart from the few examples that he tossed out to indicate his awareness of the imperfect coincidence of meaning and use. He remarked: ‘One can say: the explanation of the meaning of a word does indeed give the meaning, and the explanation is a rule for the use of a word, but we don’t say of every 29

It is striking that in §138 Wittgenstein queries how what we grasp at a stroke (the meaning of an expression) can be the same as the ‘use’ (note his scare-quotes) that is extended over time. But the use, i.e. the way of using an expression, is not spread out over time — it is the use qua applications that can be said to be spread out over time.

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rule that it determines the meaning, but only of certain ones. And I can characterise these through examples, but not by giving a general characteristic’ (MS 147, 4v). I suspect that he would have denied that the concept of meaning has precise limits. Its ragged edges are often indeterminate, and frequently context- and purpose-dependent. But at any rate, there is no reason to suppose that any philosophical investigation that Wittgenstein pursued is vitiated by his failure to plot the ragged contour lines of the concept of meaning within the scope of the concept of the rule-governed use of a word.

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

IX Contextual dicta and contextual principles 1. The problems of a principle The dictum ‘A word has a meaning only in the context of a sentence’ was ﬁrst enunciated by Frege in The Foundations of Arithmetic. It has been said to be the most important single statement Frege ever made. But that is puzzling, since taken at face value it is patently false. For we often ask what a word means outside any sentential context, and the question can typically be answered. When we want to ﬁnd out what a word means, we can look it up in a dictionary which tells us, for example, that the word ‘primatology’ means ‘the study of primates’. Formal deﬁnitions specify the meaning of a word independently of a sentential context. Furthermore, there are perfectly signiﬁcant uses of words (quite apart from one-word sentences such as ‘Jump!’) outside sentential contexts. We use personal names on labels (and may order a packet of 100 such labels with our own name printed on them for future use), stick names of substances on bottles, and put name-labels on drawers or ﬁles. It would be dogmatic to insist that ‘aspirin’ on a bottle was elliptical for ‘This bottle contains aspirin’, and no more than adherence to a form of representation to insist that although what is written on the label is a single word, it is really a one-word sentence the depth grammar of which is ‘This bottle contains aspirin’.1 We put numerals or number-words on houses, number-plates and licences, at the heads of chapters and at the foot of pages. We use single words or phrases as book titles (Persuasion), as greetings (‘Hello’), exclamations (‘Hurrah’) and as expletives (‘Damn’). We insert meaningful words in crossword puzzles, and we do not allow players of Scrabble to put down meaningless concatenations of letters, but only words of our language. And we distinguish between a list of meaningful words and a list of nonsense words such as ‘Juwiwalera’ or ‘Lilliburlero’. So if the contextual dictum is the most important statement Frege ever made, it cannot, presumably, be this that he meant to exclude. 1

Does this mean that the alleged sentence expressed a true proposition when the bottle was purchased, and a false one when one takes the last aspirin? How is one to know what exactly this allegedly one-word sentence is elliptical for or what its depth grammar is? Why is it not the very different quantiﬁed sentence ‘There is aspirin in this bottle’ or ‘There are 25 aspirin tablets in this bottle’? What would show that a word written on a bottle was not a sentence? And so on.

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On the other hand, we may grant that in a sense there is much truth to the famous dictum. After all, we may grant that a dictionary tells us all the different meanings of a word, but that to ﬁnd out what the word means in use, we must know the context of its use. ‘Coach’ may mean a person who trains sportsmen, a single-decker bus, or a horse-drawn vehicle. But to know what it means in a given use, we must know in what sentence it was embedded (or whether it was used as a one-word sentence), and in what situation the sentence was uttered. ‘White’ is a colour-name, but white coffee is brown, and a white Christmas is a snowy one. And so on. But it is evident that this is not what Frege meant to include in his famous dictum. Indeed, he viewed such phenomena as faults of ambiguity in natural languages that are to be remedied in a logically perfect language. So, we must ﬁnd out what Frege did have in mind. Frege’s dictum is often referred to as ‘the context principle’. It and its variants occur ﬁve times in the course of the Foundations (1884). But they seem to signify a variety of quite different things. In the ﬁrst occurrence the dictum signiﬁes a heuristic principle that we are enjoined to follow in order to avoid falling into the morass of psychologism and taking words to stand for ideas in the mind (FA p. x). It is not obvious, however, that virtually the only alternative to taking words to stand for ideas in the mind is to take them to have a meaning only in the context of a sentence. In the second occurrence, such a principle is invoked to shed light on the question of what it is of which we assert something when we make a statement of number. Light will be shed on the matter, Frege writes, if we ‘consider number in the context of a judgement which brings out its basic use’ (FA §46).2 That, he avers, suggests that a statement of number is an assertion about a concept. It is important to note here that the emphasis is not on a sentential context, but on the context of a judgement. Subsequently (FA §60), the dictum speciﬁes a necessary condition for a word to have a meaning (‘Only in the context of a sentence does a word have a meaning’). But, rather surprisingly, this is immediately and without argument transformed into a sufﬁcient condition (‘It is enough if the sentence taken as a whole has a sense; it is this that confers on its parts also their content’). Subsequently the dictum appears to be invoked in order to justify a procedure akin to what we call ‘contextual deﬁnition’ of number-words (FA §62). But that is apparently repudiated and the proposed paraphrastic deﬁnition in terms of one-to-one correspondence is replaced by an explicit deﬁnition (FA §68). So, surveying the different occurrences of the dictum, is there only one principle here, or are there different ones? To cap this, the contextual dictum is nowhere explicitly cited, let alone emphasized, in Frege’s masterwork of the 1890s, The Basic Laws of Arithmetic (Part I). This has been explained by the alleged fact that it was only in the 1890s that he disastrously assimilated sentences to proper names, and therewith abandoned the primacy he had assigned to sentences in the Foundations. But this is puzzling, since he patently treated 2

I am grateful to Edward Kanterian for drawing my attention to this little noticed passage.

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sentences as proper names already in Begriffsschrift in 1879.3 Furthermore, is it plausible that he should silently and without notice repudiate what was allegedly the most important statement he ever made?4 Wittgenstein apparently quotes Frege’s dictum a number of times in the Tractatus. He writes that: ‘Only propositions have a sense; only in the context of a proposition does a name have a meaning’ (‘Nur der Satz hat Sinn; nur im Zusammenhange des Satzes hat ein Name Bedeutung’ (TLP 3.3)). Again, at 3.314, he writes: ‘An expression has a meaning only in a proposition,’ and at 4.23 he adds: ‘It is only in the context of an elementary proposition that a name occurs in a proposition.’ But before jumping to the conclusion that Wittgenstein is simply endorsing Frege’s dictum, we should bear in mind that although Wittgenstein uses Frege’s terminology of ‘sense’ (‘Sinn’) and ‘meaning’ (‘Bedeutung’), he means something quite different by ‘sense’ and holds quite different principles concerning sense and meaning. For Frege held the sense of a sentence to be the thought it expresses, which is an abstract entity with which we come into contact when we think (PW 137, 145, 148 (NS 149, 157, 160)). Thinking or believing is a binary relation between a person and a thought. A thought is a mode of presentation of a meaning. It presents a truth-value (‘the True’ or ‘the False’) as the value of a function for an argument, and that truth-value is the meaning (Bedeutung) of the sentence. But for Wittgenstein, the sense of a sentence is its agreement and disagreement with the possibilities of obtaining and non-obtaining of states of affairs (TLP 4.2). Furthermore, a state of affairs is not an abstract entity; indeed, it is not an entity of any kind, but a possibility. Thinking is not a binary relation between a thinker and a thought. It is, rather, the projection of a representation on to the state of affairs it represents, and the method of projection is meaning or intending (TLP 3.11; PTLP 3.1–3.15; MS 108 (Vol. III), 218f.; see ‘Turning the examination around: the recantation of a metaphysician’, sect. 2). What we think (mean) when we think that p is not something distinct from the state 3

Frege did not say that the expression for a judgeable content in concept-script is a name. But he compared concept-script to a language in which the content of judgement is always expressed by a nominalized sentence, i.e. a complex ‘proper name’. Furthermore, he paraphrased signs of the form ‘— A’ as ‘the circumstance that A’ (BS §§2, 23), just as he later introduced the two truth-values as the objects named by sentences with the following explanation: ‘By the truth-value of a sentence I understand the circumstance that it is true or false’ (SM 34, emphasis added). Further, he said that symbols ﬂanking the identity-sign are names of contents, are representatives of their contents, and claimed that an identity-statement signiﬁes the circumstance that the two names have the same content (BS §8). The fact that Frege allowed expressions that stand for judgeable contents to ﬂank the identity-sign both in deﬁnitions (BS §§24f., 29, 31) and in judgements (BS §§25, 27f.) shows that he treated expressions for judgeable contents as names (cf. PW 35f. (NS 40)). 4 It would be inappropriate here to venture a full analysis of Frege’s context principle(s), their rationale and evolution from Begriffsschrift, through the Foundations, to the Basic Laws. Gordon Baker and I attempted this in Frege: Logical Excavations (Blackwell, Oxford, 1984), chs 8 and 10, sect. 4. The current discussion is limited to what is relevant to an understanding of Wittgenstein’s invocations of the dictum. So the fate of Frege’s context principle(s) after the bifurcation of content into sense and meaning will not be discussed here.

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of affairs the obtaining of which makes true what we say when we say that p. And while propositions have a sense thus construed, they do not, according to Wittgenstein, have a meaning. In particular, their truth-value is not their meaning. Furthermore, unlike Frege, Wittgenstein denied that simple names have a sense at all; they have only a meaning, and their meaning is the simple sempiternal object in reality for which they go proxy in the representation of a state of affairs. So we need to examine Wittgenstein’s rationale for his contextual dictum, and must not assume without more ado that he was simply endorsing whatever it was that Frege was propounding in the Foundations. Despite their differences about sense (Sinn) and meaning (Bedeutung), both Frege and the young Wittgenstein cleaved to the conception of a language as a calculus. Irrespective of what Frege thought about the forms and operations of natural languages (a controversial matter), it is evident that the concept-script he invented and conceived to be a logically perfect language was deliberately constructed on the model of a calculus. It was not for nothing that the subtitle of Begriffsschrift was ‘a formula language of pure thought modelled upon the formula language of arithmetic’. It is also patent that Wittgenstein, when he wrote the Tractatus, held any language to be a calculus. That, he conceded, is not evident from the surface grammar of a language, but it will become clear on analysis, for it is a requirement of the possibility of representation. For elementary propositions are composed of simple names, the meanings of which are simple objects. The sense of such propositions is a function of the meanings of the constituent names. From the fund of elementary propositions all propositions can be generated by the operation of joint-negation. For all propositions are truth-functions of elementary propositions. So, conceiving of language as a calculus, both philosophers construed understanding as a computational process. Frege, towards the end of his life, held that the understanding of a sentence is a process of ‘calculating’ or constructing its sense from one’s knowledge of the senses of its sub-sentential components. Furthermore, he invoked this idea in order to explain how it is that we are able to understand novel sentences. ‘The possibility of our understanding sentences we have never heard before rests evidently on this, that we construct the sense of the sentence out of parts that correspond to the words’ (letter 12 to Jourdain, 1914, PMC 79). Wittgenstein did not think that the sense of a sentence is composed of the senses of its constituents. For the simple names of which an elementary proposition consists have no sense but only a meaning. Rather, he held that the sense of a sentence is a function of the meanings of its constituent simple names. The meanings of simple signs (words) must be explained to us if we are to understand them. With propositions, however, we make ourselves understood. It belongs to the essence of a proposition that it should be able to communicate a new sense to us. A proposition must use old expressions to communicate a new sense. (TLP 4.026–4.03)

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So he may well have conceived of understanding sentences, a fortiori of understanding new sentences, as a computational process of calculating the sense of the sentence from one’s knowledge of the meanings of the constituent words (one’s ‘interpretation’ of the speaker’s meaning) and their mode of combination. In this respect, then, Frege’s late ideas and Wittgenstein’s early ones do perhaps converge. This alone would make Wittgenstein’s apparent endorsement of Frege’s contextual dictum in the Investigations §49 puzzling. For by the time he wrote the Investigations, Wittgenstein had come to repudiate the calculus conception of language root and branch, and with it the computational conception of understanding. In §81 he remarks that only when one is clear about the concepts of understanding, meaning (des Meinens) and thinking will it also ‘become clear what can lead us (and did lead me) to think that if anyone utters a sentence and means or understands it, he is operating a calculus according to deﬁnite rules’. So if a speciﬁc contextual principle lay at the heart of Wittgenstein’s calculus conception of language, how is it possible to repudiate the one without abandoning the other? But matters are even more puzzling. For his endorsement of Frege’s contextual dictum gives it an interpretation which has no obvious ground in anything Frege ever wrote. Wittgenstein’s remark runs as follows: . . . naming and describing do not stand on the same level: naming is a preparation for description. Naming is not so far a move in the language-game — any more than putting a piece in its place on the board is a move in chess. We may say: nothing has so far been done, when a thing has been named. It has not even got a name except in the language-game. This was what Frege meant too, when he said that a word has a meaning only in the context of a sentence. (PI §49)

The thought that naming is not a move in the language-game but a preparation for such moves is important and insightful. The idea that the sentence is the minimal unit by which one ‘makes a move in the language-game’ is arguably exaggerated (the linguistic signs used in greeting, hailing people by their name, cursing, and exclaiming are not necessarily or even typically one-word sentences), and although sometimes attributed to Wittgenstein, is not actually asserted by him. Be that as it may, detailed reﬂections on speech-acts (other than assertion) are conspicuously missing from Frege’s writings. Nowhere, in his discussions of his contextual dicta does he mention the thought that it is only with a sentence, and not with anything less than a whole sentence, that one can perform an act of speech.5 The contextual dicta, despite appearances to the contrary, are neither unequivocal nor clear. Arguably a number of different principles are at stake, some of which may well be true while others are false. A further point that requires elucidation is how these principles stand in relation to the 5

ⳕ

Moreover, in his formal system, to satisfy his requirements of determinacy of sense and completeness of deﬁnition, Frege held ‘–– 2’ to be well-formed (although false) and its negation ‘-ⲙ- 2’ to be truly assertible. So ‘ 2’ is a false assertion and ‘⵫ⲙ 2’ a true one (cf. BLA i §§5f.).

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Augustinian conception of language. It is all too easy to assume6 that the so-called context principle was a deﬁnitive move away from it. But, as was already noted (‘The Augustinian conception of language’, a vii and e ii), that is not obviously right. Even in the opening quotation from Augustine’s Confessions, emphasis is placed on hearing words used ‘in their proper places in various sentences’, and it is evident that Wittgenstein conceived of the Tractatus, which patently embraced some context principle or principles, as moulded by the force-ﬁeld of the Augustinian conception of language and meaning. So it is not clear that the contextual dictum is a move away from the Augustinian picture. Indeed, in the following we shall see that Frege and the young Wittgenstein invoked it in order to conﬁrm the principles that the essence of words is to name or stand for entities, that these entities are the meanings (Bedeutungen) of the words, and that sentences are combinations of words.

2. Frege Locke’s Essay Concerning Human Understanding, Book III, dominated reﬂections on language throughout the eighteenth century. Locke unequivocally took the meanings of words to be ideas in the mind, and paid scant attention to the role of words in sentences or indeed to the roles of sentences. In this he was followed, with but marginal qualiﬁcation, by Berkeley and Hume. The British empiricists (following Descartes) were remarkable for their neglect of, and contempt for, formal logic and its theoretical foundations. But it would be wholly mistaken to suppose that prior to Frege no attention whatsoever was given to sentences and their structure and to the different roles of different kinds of words in sentences. The role of sentences in the making of statements, and the necessary complexity of sentences was already noted by Plato, who observed that for any statement to be made, a combination of noun and verb is requisite.7 Aristotle emphasized that truth and falsity, afﬁrmation and denial, presuppose complexity, but that a combination of noun and verb to make up a sentence does not sufﬁce for a proposition. For it is to propositions alone (as opposed to, e.g., a prayer) that truth and falsity can be ascribed. The nouns and verbs of which propositions and other sentences are formed have a meaning, but, by themselves, lack truth or falsehood.8 This conception continued throughout the Middle Ages. Words were conceived to be essentially ‘parts of speech’ ( pars orationis), potential constituents of sentences used in speech. Peter of Spain held, in conformity with Antiquity, that ‘a proposition is a sentence signifying something true or false in the manner of a judgement, such as “A man is running”; or again, a proposition is the afﬁrming or 6 7 8

As indeed was assumed in the ﬁrst edition of this Commentary. Plato, Sophist, 262a–c. Aristotle, De Interpretatione, 16a–b.

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denying something of something’.9 The conception persisted. The Port-Royal Logic claimed that Judgements are propositions expressed by sentences . . . sentences themselves are composed of words . . . The words set apart to refer to things or modes of things are called nouns [or pronouns]. . . . A verb is nothing else but a word whose principal function is to indicate assertion . . . The indicative mood of the verb is used for this principal function. . . . The product of judging is expressed by a sentence which must contain two terms — the one term is the subject, which expresses the idea of which we afﬁrm or deny another idea; the second term is the predicate, which expresses the idea which is afﬁrmed or denied of the idea expressed by the subject.10

Standard logical textbooks began from consideration of terms or concepts (vide Kant’s Jäsche lectures on logic), proceeded to a discussion of judgements, held to be composed of terms, and ﬁnally moved on to consider inferences. This conception was still accepted wisdom, and this order of exposition was still being repeated, in the nineteenth century by almost all authors of books on logic writing before, or at the same time as, Frege wrote his great logical works. So Frege’s innovation was obviously not to draw attention for the ﬁrst time to the diversity of the parts of speech, or to the signiﬁcance of structure, or to the role of sentences in the expression of a judgement. What, then, was it? Frege spelled it out quite clearly, both at the beginning of his career and at the end of it. In 1880/1 he wrote, ‘I start out from judgements and their contents, and not from concepts . . . I allow the formation of concepts to proceed only from judgements. . . . Instead of putting a judgement together out of an already previously formed concept as a predicate, we do the opposite and arrive at a concept by splitting up the content of a possible judgement’ (PW 16f. (NS 17)). In his ‘Notes for Ludwig Darmstaedter’, written in 1919 and intended to give an overview of his life’s work, he wrote: What is distinctive about my conception of logic is that I begin by giving pride of place to the content of the word ‘true’, and then immediately go on to introduce a thought as that to which the question ‘Is it true?’ is in principle applicable. So I do not begin with concepts and put them together to form a thought or judgement; I come by the parts of a thought by analysing the thought. This marks off my conceptscript from the similar inventions of Leibniz and his successors.11 (PW 253 (NS 273)) 9

Peter of Spain, Summulae Logicales, 1.07. A. Arnauld, The Art of Thinking, tr. J. Dickoff and P. James (Bobbs-Merrill, Indianapolis, 1964), Pt. II, chs 1–3. 11 See also his correspondence with Jourdain in 1910: ‘To found the “calculus of judgments” on the “calculus of concepts” (which is properly a “calculus of classes”) is to reverse the correct order of things; for classes are something derived, and can only be obtained from concepts (in my sense) . . . calculations with classes must be founded on the calculation with concepts. And the calculation with concepts is itself founded on the calculation with truth-values (which is better than saying “calculus of judgements”)’ (PMC 192, n. 71). 10

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Obviously this is not a doctrine about the nature and order of conceptacquisition by the language-learner. It concerns logical analysis for the purposes of the science of the laws of truth. Giving ‘pride of place’ to the word ‘true’ was no innovation (Aristotle had already done that); nor was there any novelty in introducing the thought (or the content of a judgement) as that which is true or false (this too was part of the traditional conception of logic). But in traditional logic, the science of terms (their classiﬁcation and the determination of their various roles) precedes the science of judgements and inferences. Frege is emphasizing, in the above two passages, that in his novel function-theoretic logical system he reverses that order. In logical analysis, unjudgeable contents originate from the decomposition of the contents of a possible judgement. We start out with judgements, not with their constituents, and we decompose them in various ways by function/argument analysis into unjudgeable contents. (In his mature logical system, in which content is split into sense and meaning, he starts out with thoughts and decomposes them into their constituents, viz. the senses of proper names, the senses of concept-words and of higher-level function-names.) It should be noted that this analytical strategy is applied in the ﬁrst instance to possible judgements, and only derivatively to sentences that may be used to express them. They are decomposed not into subject and predicate, but into argument and function. So, for example (PW 16f.), the judgement that 24 = 16 may, by functional abstraction, yield the concept fourth root of 16 (x4 = 16) or the concept logarithm of 16 to the base 2 (2x = 16) or the concept relation of a number to its fourth power (x4 = y). But the sentence in natural language ‘Two to the fourth equals sixteen’ cannot yield such a rich harvest by decomposition. In the Foundations we are told that the content of the judgement ‘line a is parallel to line b’ can ‘be carved up’ so as to yield the concept of identity of direction (FA §62), although, to be sure, the sentence ‘line a is parallel to line b’ contains neither an identity-sign nor the word ‘direction’. With this analytical, decompositional strategy in mind, we can now approach Frege’s successive invocations of his context principle (or principles) in the Foundations. We must bear in mind that in this book, Frege uses the terms ‘content’, ‘meaning’ and ‘sense’ more or less interchangeably, and that the notion of content was explicitly restricted in Begriffsschrift to what is relevant to the cogency of inference (BS §3).12 The ﬁrst occurrence of the dictum in the Foundations is in the Preface, where Frege declares the three methodological principles that inform the book. The ﬁrst principle is an anti-psychologist one: 12 Thus: ‘In my formalized language . . . only that part of judgements which affects the possible inferences is taken into consideration. Whatever is needed for a valid inference is fully expressed; what is not needed is for the most part not indicated either’ (ibid.). This is what Frege calls ‘the conceptual content of the judgement’ (BS §4). Hence the content (or meaning) of a subsentential expression consists only in its contribution to the conceptual content of the judgement expressed by the sentence. Obviously, outside any sentential context words make no such contribution to the contents of judgement (see below).

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always to separate the psychological from the logical. The second is the heuristic context principle: ‘never to ask for the meaning of a word in isolation, but only in the context of a sentence’.

Frege links the two, inasmuch as the rationale for the heuristic principle is that if it ‘is not observed, one is almost forced to take as the meanings of words mental pictures or acts of the individual mind, and so to offend against the ﬁrst principle as well’ (FA p. x). Frege resisted the idealist (psychologist) drift to which others, such as the British empiricists and the German psychologicians, had succumbed. But, in truth, there is no good reason to suppose that asking what a given word, e.g. ‘procrastinate’ or ‘million’ means outside any sentential context must incline one to suppose that it has an idea as its meaning, and Frege gives none. Moreover, by the end of his own investigation into number, Frege himself offers us explicit deﬁnitions, i.e. deﬁnitions outside any sentential context, of number-words such as ‘nought’ and ‘one’, e.g. ‘0 is the number which belongs to the concept “not identical with itself ” ’ (FA §74; cf. §76).13 The second occurrence of a context principle is in §46, in which we are invited to consider number in the context of a judgement (im Zussammenhange eines Urteils) of a kind that brings out the basic use of statements of number (Zahlangabe) that make a judgement of number (Zahlurteil). For it will then become clear that statements of number, such as ‘There are four companies’, ‘There are 500 men’ or ‘Venus has 0 moons’, assign numbers to concepts (FA §48). This ﬁts well the association of context principles with the fundamental insight of Frege’s whole philosophy: namely, the primacy of judgements over concepts for purposes of logical analysis and the various ways of precipitating concepts out of judgements by functional abstraction. The third occurrence of the dictum is in §60, in which Frege ﬁrst presents it in the form of a restrictive condition: ‘Only in a proposition (Satz) have the words really a meaning’.

We have already noted that this principle is patently false as far as our ordinary conception of meaning is concerned; but there is no reason for thinking that Frege had that in his sights. What he is primarily concerned with are inference-relevant features of expressions. He emphasizes here again that the presence or absence of any associated ideas is irrelevant to the question of whether a word has any meaning. That we do not associate a word with an idea as its meaning or content, Frege insists, does not mean that we ‘thereby forfeit the 13

To be sure, this looks like a sentential context, but it is clearly intended as a deﬁnition (cp. FA §67), viz. ‘0’ = df ‘the number which belongs to the concept not identical with itself ’.

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support we need for our inferences’ (ibid.). But he immediately moves on to a much stronger sufﬁciency principle, viz. ‘It is enough if the proposition (Satz) taken as a whole has a sense; it is this that confers on its parts also their content’ (ibid.).

The transformation of what appears to be a necessary condition for a word to have a meaning into a sufﬁcient condition is striking. Again, what he has in mind is that the fact that we associate no idea with the number 0, for example, does not imply that in the sentence ‘The number of moons of Venus is 0’ the numeral has no meaning. For we can draw legitimate inferences from this proposition (e.g. that the number of moons of Venus is less than 10). However, taken au pied de la lettre, the sufﬁciency principle is not obviously correct: ‘It is raining’ has a sense, but that does not sufﬁce to confer content on the word ‘It’ in this sentence, in which it functions merely to satisfy a syntactical requirement. To be sure, Frege would brush this aside as irrelevant to his concerns — as indeed it is. But that is no thanks to the sufﬁciency principle. Frege proceeds to elaborate: ‘The self-subsistence which I am claiming for number is not to be taken to mean that a number word signiﬁes something when removed from the context of a proposition (Satz), but only to preclude the use of such words as predicates or attributes, which appreciably alters their meaning’ (ibid.). In the sentence ‘The number of moons of Jupiter is four’, ‘four’, according to Frege, is the proper name of a number, i.e. of a mathematical object. But in its adjectival occurrence, e.g. ‘Jupiter has four moons’, ‘four’ is merely part of a compound predicate14 and does not stand for an object. This does shed a little more light on Frege’s invocation of contextual dicta. It seems patent that he thought that what meaning an expression has in a sentence depends on how the sentence is ‘carved up’. So ‘four’ in some sentences may have the number four as its meaning, and in others not. (So too, ‘Vienna’ in the sentence ‘Vienna is the capital of Austria’ has an object, namely the city, as its meaning; but in the sentence ‘Trieste is no Vienna’, it does not fulﬁl the function of a proper name at all, but is part of a function-name that has a function (concept) as its meaning (CO 200f.).) Frege’s reasoning is that despite the fact that number-words do not stand for ideas or intuitions that are given to us, nevertheless they do stand for objects when they occur non-attributively in sentences. The sufﬁciency principle is in fact invoked precisely to conﬁrm the idea that the number-words, as they occur in sentences of the form ‘The number of Fs is n’, are names, that they have a meaning, and that their meaning is the object they stand for. So, considered from the point of view of the Augustine’s picture of language and the 14

Having already established to his satisfaction that statements of number are statements about concepts, Frege construes ‘Jupiter has four moons’ as equivalent to ‘the number four belongs to the concept moon of Jupiter’, in which the number-word occurs as part of the phrase ‘the number . . . belongs to’ (cf. FA §56).

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family of ideas that grow out of it, it is evident that Frege’s invocation of the contextual sufﬁciency principle does not distance him at all from the Augustinian conception of meaning. In §62 Frege invokes his contextual dictum to justify giving a paraphrastic deﬁnition of number-words.15 Since numbers are not ‘given to us’ in the form of ideas or intuitions, we can obtain the concept of number only by ﬁxing the sense of a numerical identity. Since it is only in the context of a sentence that words have any meaning, our problem becomes this: To deﬁne the sense of a sentence in which a number-word occurs. . . . When we have . . . acquired a means of arriving at a determinate number and of recognizing it again as the same, we can assign it a number word as its proper name.

We can assign number-words a meaning only indirectly, by giving a deﬁnition of ‘the number which belongs to the concept F is the same as the number which belongs to the concept G’, which will not mention the phrase ‘the number which belongs to the concept F’. This does not give any argumentative support to the restrictive condition, but takes it as given. It is noteworthy that the problem to be solved is to explain the sense of a sentence in which a number-word occurs, and that this is to be accomplished by picking out for each number-word a determinate object which can be assigned to it as its content (Inhalt). Despite this, Frege subsequently faults his initial deﬁnition in terms of one–one correspondence, and replaces it with an explicit deﬁnition of number-words in terms of extensions. The ﬁnal occurrence of the dictum in §106 merely recapitulates what Frege takes himself to have established. It is clear that contextual dicta are invoked in The Foundations of Arithmetic for different purposes, and that there are different principles involved: the generation of concepts by functional decomposition of possible judgements, a heuristic principle, a restrictive condition and a sufﬁciency principle. The dictum that a word has a meaning only in the context of a proposition (signiﬁcant sentence) is associated with a particular conception of what it is to assign a meaning to a proper name, and with a general conception that ties the meaning of a word in a given sentence to the impact of this word on the legitimacy of inferences incorporating the judgeable content of that sentence. It is also clear that Frege was not concerned here with the nature or order of language-learning and concept-acquisition; nor was he concerned with speech-acts and the idea that the sentence is the minimal unit for ‘making a move in the language-game’. Rather, it was the sentence as the vehicle of judgement that concerned him. The primacy of judgement in logical analysis was because the contents of judgement (no matter whether asserted or unasserted) are the bearers of truth, and logic is the science of the laws of truth. What marked 15

Frege’s conception of his paraphrastic deﬁnitions was not reductive, unlike the modern conception of contextual deﬁnitions.

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off Frege’s procedures from the Aristotelian tradition was not this, but rather the idea of the analytic decomposition of judgeable contents into function and argument, by contrast with the traditional synthetic conception of judgeable contents as assembled out of terms (subject and predicate).

3. The Tractatus We noted above that Wittgenstein seemingly endorses Frege’s contextual dictum that a word has a meaning only in the context of a sentence at 3.3, 3.314 and 4.23. But, as was observed, this apparent convergence must be taken with a pinch of salt, since Wittgenstein’s conception of sense, as well as his conception of the relationship between sense and meaning, is altogether different from Frege’s. Furthermore, Wittgenstein did not have Frege’s functiontheoretic motive for a contextual principle. His conception of propositional functions was closer to Russell’s than to Frege’s. He did not countenance alternative functional decomposition of judgements as Frege, in appropriate cases, did, but cleaved to the uniqueness of analysis. He did not take propositional functions to be functions from objects to truth-values, and did not take truthvalues to be objects of any kind. Whence, then, Wittgenstein’s insistence that names have a meaning only in the context of a sentence? It was motivated by the picture theory of the proposition, on the one hand, and by the attendant metaphysics of symbolism, on the other. One inspiration of the picture theory was the analogy between a proposition and a model of a historical state of affairs, e.g. a model of a trafﬁc accident that utilizes toy cars and toy people to depict the disposition of the cars and people in a trafﬁc accident (NB 7). Here it is perspicuous that a toy vehicle and a toy person only represent N.N.’s car and N.N. in such-andsuch an accident when the toys are arranged in a tableau vivant of the accident. When the toys are put back in their box, they represent nothing whatsoever. So representing tokens represent only when they are elements of a representation. And, it seemed, a representation is a fact. For it is the fact that the elements are arranged as they are that says that the represented objects are arranged thus-and-so (TLP 2.12–2.15). So if we are to conceive of a proposition as a picture or model of a situation, then it may seem plausible to argue, as Wittgenstein did, that the elements of the representation go proxy for the elements of what is represented, just as do the elements of the tableau vivant (TLP 4.0311). Moreover, what represents is not the names simpliciter, but the fact that they are arranged as they are (TLP 3.14, 3.142). It is only facts that can depict facts, and it is only simple names that can represent simple objects. The simple names represent simple objects only when they are constituents of a representing fact, i.e. a sentence, for only a fact can be a picture or model of a state of affairs. So, the motivation behind Wittgenstein’s endorsement of a context principle is patently picture-theoretic, and, as such, very different from Frege’s.

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Among other things, his concern in his account of the role of names in elementary propositions is not primarily with inference-relevant features, since elementary propositions can be true or false as the case may be and everything else remain the same. They are bipolar, occupy a position in logical space, and are bases for truth-functional operations. The role of a simple name in an elementary proposition is to go proxy for the object that is its meaning. The logical multiplicity of the representing fact is identical with the logical multiplicity of the state of affairs it depicts, and the form of the representing fact is the form of what is represented. The form of a constituent name in a proposition is the form of the object that is its meaning. But outside the context of a proposition, a name stands for nothing (fulﬁls no representative role), and contributes nothing to the determination of the sense of a sentence, i.e. to the depiction of a possible state of affairs. Hence Wittgenstein’s invocation of a context principle, far from distancing him from the gravitational ﬁeld of the Augustinian conception of meaning, brings him (like Frege) even more deeply into it.16 For every expression in a well-formed elementary proposition is a simple name, the meaning of a simple name is the object it represents, and the context principle, thus interpreted, asserts that every name has a meaning in the context of a sentence with a sense. And sentences are indeed essentially complex. They are combinations of names, and the essential function of such combinations is to describe possible states of affairs.

4. After the Tractatus Moore reports Wittgenstein’s comments on a contextual dictum in his 1930–3 lectures as follows: On the statement ‘Words, except in propositions, have no meaning’ he said that this ‘is true or false as you understand it’; and immediately went on to add that, in what he called ‘language games’ single words ‘have meanings by themselves’, and that they may have meaning by themselves even in our ordinary language ‘if we have provided one’. In this connection he said . . . that he had made a mistake (I think he meant in the Tractatus) in supposing that a proposition must be complex. He said the truth was that we can replace a proposition by a simple sign, but that the simple sign must be ‘part of a system’. (M 54)

Here his main concern appears to have been the denial of the essential complexity of the proposition — a doctrine to which both Frege’s function-theoretic analysis and his own picture-theoretic analysis were, for very different reasons, committed. Frege’s function-theoretic apparatus and the picture-theoretic apparatus of the Tractatus were not descriptions of the facts concerning language, but forms of representation imposed upon the facts. The idea that it is 16

With the qualiﬁcations noted in ‘The Augustinian conception of language’, sect. 6.

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of the essence of the proposition to be complex, to be composed of function and argument, or to be composed of names the logical multiplicity of which necessarily reﬂects the logical multiplicity of the state of affairs represented was not a discovery, but a requirement. This theme is later picked up in Investigations §§19f. In language game (2), ‘Slab’ is a word and a sentence, and in that language-game it is not an elliptical sentence (see Exg. §§19f.). In Philosophical Remarks Wittgenstein noted: ‘A word has a meaning only in the context of a sentence: that is like saying only in use is a rod a lever. Only the application makes it a lever’ (PR 59). He opened the Big Typescript with the remarks: Can one understand anything other than a proposition (Satz)? Or: is it not a proposition only when one understands? So: can one understand anything other than as a proposition? . . . It is important here that, in a certain sense, there are no half propositions. That is, of half sentences the same holds as of words, that they have a meaning / sense / only in the context of a sentence. (BT 1)

He elaborated this rather differently in the reworking of this material in the Grosses Format: ‘Doesn’t understanding start only with a proposition, with a whole proposition? Can you understand half a proposition?’ — Half a proposition is not a whole proposition. — but what that means can perhaps be understood as follows. Suppose a knight’s move in chess was always carried out by two movements of the piece, one straight and one oblique; then it could be said ‘In chess there are no half knight’s moves’ meaning: the relation of half a knight’s move to a whole knight’s move is not the same as that of half a bread roll to a whole bread roll. We want to say that it is not a difference of degree. (MS 140, 1 = PG 39; cf. LWL 114)

These reﬂections are attempts to extract something substantial from the contextual dictum, now freed from the encumbrances of function-theoretic and picture-theoretic considerations. This theme occurs in the Investigations too, namely in §49: naming is not a move in the language-game, but only a preparation for such a move. Ostensive teaching of the names ‘slab’, ‘pillar’, ‘block’, ‘beam’ in language-game (2) is essentially preparatory for the use of these words in orders or requests to pass the appropriate building pieces. Naming is akin to putting a chess piece on the board; ordering a slab is akin to making a move in the game. With such exceptions as were previously mentioned (above, sect. 1), a sentence is the appropriate instrument for making a move in the language-game. Earlier, Wittgenstein had written that it is only in the context of a sentence that a word has a function (MS 110 (Vol. VI), 111). Again, this is not altogether true. But one might say that it is only in the context of a sentence that a word plays a role in saying something (LWL 45). This insight is akin to Bentham’s, when he wrote:

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By anything less than an entire proposition, no communication can have place. In language therefore the integer to be looked for is an entire proposition — that which logicians mean by the term logical proposition. Of this integer no one part of speech, not even that which is most signiﬁcant, is anything more than a fragment; and in this respect, in the many worded appellative, part of speech, the word part is instructive. By it an intimation to look out for the integer of which it is a part may be considered as conveyed.17

We can greet someone, curse, cheer or blaspheme by using a single word that is patently not a sentence, not even a one-word sentence. But, as had been pointed out many centuries ago, words (with a few such trivial exceptions) are essentially pars orationis. It is with sentences that we actually say something, and what we thereby say can be reported in the appropriate structures of indirect speech, e.g. that-clauses, WH-clauses, inﬁnitives. A sentence is akin to a move in a game of chess, and using a sentence to do something is akin to making a move in a game. But a move is a move only in the context of a game. One cannot make just one move in a game and not know how to make any other. One may know what a sentence in an alien language means, but it does not follow that one understands the sentence (at least in one use of this ﬂuid concept). For mastery of a language is the background against which it makes sense to speak of understanding individual utterances (as opposed to using them parrot-wise out of a phrase-book for travellers which tells one what they mean). Hence ‘To understand a sentence means to understand a language. To understand a language means to be master of a technique’ (PI §199; cf. PG 170 –2; BB 5).

5. Compositional theories of meaning It was noted above that Wittgenstein in the Tractatus raised the question of how it is possible to understand sentences we have never heard before. He implicitly offered a computational answer. The sense of a sentence is not a function of the senses of its constituent expressions (since the simple names have no sense), nor is it composed of the meanings of its constituent expressions. For the sense of a sentence is not a complex composed of meanings, but a possibility, which has meanings, i.e. simple objects, as constituents. So it is a function of those meanings. And, Wittgenstein may have implied (TLP 4.026– 4.03, quoted above), we understand sentences, including sentences we have never heard before, by ‘calculating’ their sense from (our knowledge of ) the meanings of their constituents and their mode of combination. How precisely this unconscious process is carried out would (presumably) be a matter for psychology to investigate (cf. CL 68). 17

J. Bentham, Chrestomathia, ed. M. J. Brown and W. H. Burston, repr. in Collected Works of Jeremy Bentham (Clarendon Press, Oxford, 1983), Appendix IX, p. 400.

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In The Basic Laws of Arithmetic, where he split judgeable contents into sense and meaning (Bedeutung), Frege held that the senses of sub-sentential constituents consisted in their contribution to the determination of the sense of the sentence, i.e. to the thought expressed by the sentence. ‘If a name is part of the name of a truth-value, then the sense of the former name is part of the thought expressed by the latter name’ (BLA i §32). Towards the end of his life, Frege went considerably further in the direction of such a compositional conception of thoughts (or propositions). For he now claimed not only that a thought is composed of the senses of sentential constituents, but that the senses of sentential constituents are ‘thought-building-blocks’ (Gedankenbausteine (PW 225, cf. 243 (NS 243, cf. 262))). It is noteworthy that there is a grave tension between the decompositional conception that is involved in the priority of judgement over concepts and the synthetic conception of thoughts as composed of thoughtbuilding-blocks.18 As noted, Frege then invoked the thought-building-block

18

Frege’s rudimentary computational conception of understanding dates from 1914. He wrote:

It is remarkable what language can achieve. With a few sounds and combinations of sounds it is capable of expressing a huge number of thoughts, and, in particular, thoughts which have not hitherto been grasped or expressed by any man. How can it achieve so much? By virtue of the fact that thoughts have parts out of which they are built up. And these parts, these building blocks, correspond to groups of sounds, out of which the sentence expressing the thought is built up, so that the construction of the sentence out of parts of a sentence corresponds to the construction of a thought out of parts of a thought. And as we take the thought to be the sense of a sentence, so we may call a part of a thought the sense of that part of the sentence which corresponds to it. (PW 225, NS 243)

It is perhaps signiﬁcant that this late compositional conception of thoughts correlative to a computational conception of understanding post-dates Frege’s meetings with Wittgenstein in December 1913. For Wittgenstein had adopted a computational conception of understanding sentences earlier in 1913 (NB 98, 104) and may have discussed it with Frege when they met. This conception of understanding with its correlative explanation of how we can understand sentences we have never heard before was incorporated into the Tractatus (TLP 4.02– 4.03). Frege published his reﬂections on this matter only in 1923, in ‘Compound Thoughts’ (CP 390). What he did not appear to notice is that the compositional conception of thoughts as constructed out of thought-building-blocks is inconsistent with the decompositional analysis that is the backbone of his function-theoretic logical system and the root of his contextual principles. His late conception presupposes strict isomorphism between sentence and thought, which is inconsistent with his own decompositional analysis. (The sentence ‘line a is parallel to line b’ cannot be decomposed into ‘the direction of line a’, ‘the direction of line b’, and the name of the binary relation (function) of identity (FA §64, see below), let alone into the pair of arguments and function; nor can the sentence ‘Cato killed Cato’ be decomposed into ‘Cato’ and ‘killing oneself ’, let alone into Cato and the concept (unary function) of committing suicide (BS §9)). Frege was committed to the possibility of decomposing certain judgeable contents or thoughts in irreducibly different ways into function and argument, rather than conceiving of them as built up synthetically from ﬁxed ‘thoughtbuilding-blocks’. Decompositional analysis was, in his view, more ﬂexible and versatile than the synthetic conception it was designed to replace, revealing richer logical forms and novel forms of concept-formation, and consequently could perspicuously represent a far wider range of legitimate inferences. For discussion of the tension between the two conceptions, see G. P. Baker and P. M. S. Hacker, Frege: Logical Excavations (Blackwell, Oxford, 1984), pp. 381ff.

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conception to explain the possibility of our understanding sentences we have never heard before. For, he now suggested, we construct the sense of the novel sentence out of parts that correspond to the words (PMC 79, 12th letter to Jourdain). From the 1960s the question of how we can understand sentences we have never heard before came to preoccupy philosophers of language and theoretical linguists. How we can produce and understand novel sentences was referred to, rather misleadingly, as the problem of the ‘creativity of language’ (there is nothing obviously creative about saying and understanding someone else’s saying ‘The teddy is in the fridge’, and the misnomer screens from sight genuine creativity, i.e. originality, in the use of language, e.g. Schelling’s metaphor ‘Architecture is frozen music’). It is likely that the inspiration for the ensuing theorizing was derived from the few enigmatic remarks on the matter in the Tractatus. Philosophers and linguists agreed that the answer to the question of how we can understand novel sentences lay in a computational conception of understanding. So Chomsky, for example, argued that ‘For a person to understand a linguistic expression, the mind/brain must determine its phonetic form and its words and then use the principles of universal grammar and the values of the parameters to project a structured representation of this expression and determine how its parts are associated.’19 Philosophers followed suit in respect of both compositionalism and computationalism. Davidson wrote: An acceptable theory should . . . account for the meaning (or conditions of truth) of every sentence by analysing it as composed in truth-relevant ways, of elements drawn from a ﬁnite stock . . . the theory [should] provide a method for deciding, given an arbitrary sentence, what its meaning is. (By satisfying these two conditions a theory may be said to show that the language it describes is learnable and scrutable).20

And Dummett claimed that the fact that anyone who has a mastery of any given language is able to understand an inﬁnity of sentences of that language, an inﬁnity which is, of course, principally composed of sentences he has never heard before . . . can hardly be explained otherwise than by supposing that each speaker has an implicit grasp of a number of general principles governing the use in sentences of words of the language . . . an explicit statement of those principles an implicit grasp of which constitutes the mastery of the language would be, precisely, a complete theory of meaning for the language.21

19

N. Chomsky, Language and the Problems of Knowledge (MIT Press, Cambridge, Mass., 1988), p. 136. 20 D. Davidson, ‘Semantics for Natural Languages’, repr. in Inquiries into Truth and Interpretation (Clarendon Press, Oxford, 1984), p. 56. 21 M. A. E. Dummett, ‘Can Analytic Philosophy be Systematic and Ought it to be?’, in Truth and Other Enigmas (Duckworth, London, 1978), p. 451.

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It is striking that nowhere in his later work does Wittgenstein discuss the problem that he had raised and to which he had proposed a solution in the Tractatus. The moot question is whether that is because he thought that his original solution stood ﬁrm, despite the collapse of the calculus conception of language and the picture theory of representation, or whether it is because he thought that the original problem was bogus, being rooted in fundamental misconceptions of understanding, of meaning, and of the relation between sentence-meaning and word-meaning. It would be exceedingly implausible to suppose the former, since it is patent that the compositional view of sentencemeaning is inconsistent with Wittgenstein’s later conception of meaning, the idea that a language is a calculus is inconsistent with his later conception of language, and the computational conception of understanding is inconsistent with his later description of the grammar of ‘understanding’. This is not the forum in which to confront computational theories of understanding in a systematic manner.22 But it is appropriate to clarify why they represent a road down which Wittgenstein would not have gone, and to elucidate the bearing that his reﬂections on meaning and understanding have on the misleading question of how we can understand sentences we have never heard before. It is patent that Wittgenstein would have challenged the idea that the sense of a sentence, i.e. what is said by the use of a sentence on an occasion, is composed of the meanings (or senses) of its constituent expressions. The meaning of an expression is not a kind of ‘entity’ (not even a so-called abstract entity). It is, with due qualiﬁcation, its use; and it is given by an appropriate explanation of meaning. Such an explanation of meaning is in effect a rule for the use of the explanandum. But it makes scant sense to suggest that what is meant by an utterance (a sentence in use) is composed of the uses of its constituent words. Nor can it be said that the meaning of an utterance is composed of the rules for the use of its constituent expressions. Indeed, what is said by the use of a sentence cannot be said to be composed of anything. It is what is explained by an appropriate paraphrase. But there is no canonical method of paraphrase, and typically various paraphrases are acceptable. Wittgenstein did not hold that the meaning of a word consists in its contribution to the determination of the truth-conditions of any sentence in which it might occur. First, he never used the term ‘truth-conditions’ in the post-Tarskian manner (see above, pp. 67 and 138f.). In the Tractatus, the truth-conditions of a molecular proposition are the conditions the proposition has to satisfy in order to be true (i.e. those assignments of truth-values to its constituent elementary propositions that will make it true). But it makes no sense to speak of the truth-conditions of an elementary proposition (i.e. of the truth-value assignments that are a condition for its being true). A fortiori, he did not cleave, 22

For a detailed discussion of the incoherences involved in the computational conception of understanding, see G. P. Baker and P. M. S. Hacker, Language, Sense and Nonsense (Blackwell, Oxford, 1984), ch. 9. The following pages make use of materials from this longer discussion.

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in his later philosophy, to the central contextual principle of late twentiethcentury philosophy of language, that the meaning of a word consists in its contribution to the determination of the truth-conditions of any sentence in which it may occur.23 Secondly, he rejected the idea that every sentence consists of a sentence-radical and a force-operator (see Exg. §22 and page 11/9n.; also ‘Descriptions and the uses of sentences’). But if it is incoherent to suppose that every sentence, including imperatives and interrogatives, has a truth-valuebearing descriptive component, then accounting for the meaning of words in terms of their contributions to the truth-conditions of sentences in which they may occur immediately implies that in non-declarative sentences those words have either a different meaning or no meaning at all, which is absurd. The compositional picture is derived from a conception of the modern calculus of logic as revealing the depth grammar of any possible language. It presupposes that the meaning of a word is given by speciﬁcation of the conditions that are necessary and sufﬁcient for its application. In the case of deﬁnables, the meaning of a word is given by an analytic deﬁnition (e.g. in terms of characteristic marks). In the case of so-called indeﬁnables, a different story has to be told (but rarely is). It is patent that Wittgenstein, in his later work, did not accept this picture. It had been part of the Tractatus conception, and he now repudiated it — hence his lengthy investigations into ostensive deﬁnition, the uses of samples, family-resemblance concepts and their explanation by examples, vagueness and its legitimacy for hosts of concepts, categorial concepts and their roles, and so on. His investigations into rules of language, and his emphasis on the fact that they do not budget for all cases, that they are often open and commonly ﬂexible, and on the differences between rules of grammar and rules of a calculus are indicative of the extent to which he wished to distance himself from the conception of language as a calculus. So too does his insistence on the various forms of context-dependency of the meanings of utterances, on the speciﬁcity of the particular case which is to be explained in its context, and on the impossibility of laying down perfectly general, context-free, algorithmic rules to differentiate sense from nonsense. In the spirit of the later Wittgenstein’s reﬂections on language and meaning, we can elaborate four general areas of difﬁculty for compositional accounts of sentence-meaning. (i) Word clusters and analogical relations. Wittgenstein stressed the pervasive role of analogy in language. That insight can brought to bear on the compositional conception of meaning. We speak of animals running, taps running, rivers running, paint running, stains running, routes running (from X to Z via Y), and of politicians in America running for ofﬁce (in Britain they just stand). We distinguish a bachelor from a bachelor of arts, a knight-bachelor from a bachelor seal. We talk of a person’s foot, the foot of a mountain, the foot of 23

But that is not because he claimed that it consists in its contribution to something called ‘its assertion-conditions’. He made no such claim.

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a page, and of the measure one foot. In such cases we have a word cluster, a network of interrelated terms woven together by different patterns of analogy. The expressions in each cluster are related, but it is not obvious that the meaning of a given expression within a cluster can always be represented as derived by a set operation from another. In particular, the analogies involved are not regular and predictable. It will avail little to attempt to account for members of a given ﬁeld by embedding an ‘analogy operator’ in the analysis, e.g. ‘Φ*b’ = ‘b doing-something-similar-to-what-a-does when Φa’. First, it is not evident that there always is a ‘central case’. Secondly, there is no way of circumscribing the operative similarity. We talk of bachelor seals, but not of bachelor dogs. We talk of the foot of a mountain, but its foothills, not its feet. Although the engine of a car may run (idle), the car does not run (although it may be running in, or running well (i.e. its engine is functioning well) and an owner can be said to run a car). No compositional, algorithmic, generative theory of meaning can specify general rules that will determine which analogies give rise to signiﬁcant word-combinations, and if there is any hidden regularity that an ingenious linguistic theorist might discover, it is just that: a regularity, not a rule that we use to guide us or invoke to explain what a phrase means. (ii) Figurative meaning. Our language, including that of science, is run through with verbal ‘pictures’ (Benthamite archetypes). Perhaps these begin their life as metaphors. But they rapidly become fossilized, cease to be metaphors, and become part of the regular currency of language. This is especially obvious in discourse concerning the mind. Our language concerning intellection, volition and affection is largely composed of ﬁgurative expressions. Ideas strike, impress or shake us. Our memories are engraved upon our mind, things are dimly or vividly recollected. We have ﬂashes of insight, sparks of wit, ﬂights of fancy. Our spirits sink low, we drown in sorrow or plunge into an abyss of grief. Our attitudes are stiff, our passions blind, our will steely. The phenomenon of ﬁgurative meaning is ubiquitous, and there are no general principles (as opposed to ad hoc enumeration of cases) which yield a set of generative rules that show how such-and-such combinations of words are generated from such-and-such elements, and others debarred. However, ad hoc enumeration does not show that we are dealing with ambiguity simpliciter, since the relevant associations are not coincidental. (iii) Metaphor. It is obvious that metaphor will be problematic for any attempt to account for the meanings of sentences as composed of the meanings of their constituent expressions. One may be tempted to brush metaphor aside as ‘merely poetic’, involving ‘secondary or derivative meaning’, and to restrict one’s attentions to language as used for scientiﬁc purposes. This is doubly misleading. First, large areas of scientiﬁc research progress by means of fruitful metaphor or analogy, e.g. the hydrodynamic model for electrical theory. Secondly, it is not generally true that metaphor involves different word-meanings. ‘Life is a tale told by an idiot’ does not employ any word in a different meaning from its customary one. Metaphor is not standardly explained by explaining

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the meanings of constituent words and their mode of combination. ‘Architecture is frozen music’ would not be thus explained, but it resonates powerfully and is readily grasped. If it had to be explained, the explanation would be analogical, and if someone did not understand it, he would be exhibiting a form of ‘meaning-blindness’. (iv) Category restrictions. Wittgenstein repudiated the idea that categories are in general sharply deﬁned (cf. Exg. §29). The test of substitutability salva signiﬁcatione for common category membership is futile. If an account or theory of meaning is to demonstrate the derivability of every meaningful expression from deﬁned primitives by means of various operations, it must also ensure that the calculus does not produce meaningless expressions. ‘The cow ate the cabbage’ is meaningful, and prima facie has the same form as ‘The cabbage ate the cow’. But is the latter meaningful? If one wishes to argue that it is meaningful but false, then one must explain what it would be for it to be true. And here it is no use saying, ‘You know what “cabbage” means, you know what “ate” means, and you know what “cow” means, so you must know what “the cabbage ate the cow” means.’ For that uses as a premiss the conclusion which is to be established. If the calculus theorist agrees that it is meaningless, he must show that it violates combinatorial rules. He might do so (e.g. in ‘ξ eats’ only the name of an animate creature can occupy the argument place). But it is none too easy (what of ‘Acid eats metal’?). Moreover, it is only possible on the assumption that categories are sharply circumscribed. But, if Wittgenstein is right, they are not. These four objections indicate some of the difﬁculties facing any attempt to reconstruct natural language in the form of a calculus of axioms (deﬁnitions of primitives), with formation and transformation rules that can generate all well-formed sentences of the language and also specify their meanings. With sufﬁcient ingenuity and a high-minded attitude to common concepts and our shared grasp of what does and does not make sense, the calculus theorist will endeavour to confront them. A complex theory, together with a bold degree of regimentation, may be devised. But there will be a high price to pay. Our judgements about what constitutes a meaningful expression may be rejected. Explanations of meaning in the model may obliterate the subtle networks of ramifying analogies that give the soul of our language. Metaphor may be pushed aside as derivative and unimportant. Categorial nonsense may be ruled to be sensible. We need not, for current purposes, follow through the tactical manoeuvres of each side in this conﬂict. Quite apart from the difﬁculties mentioned, there are objections of principle to the enterprise. First, the explanations of meaning of compound expressions by generative rules will, for the most part, be divorced from our common explanations. For although we may sometimes explain the meaning of a sentence in terms of its structure and the meanings of its constituents, we do not typically do so. In many cases such an explanation would actually be illegitimate and useless. Numerous other kinds of explanation (by paraphrase, by analogy, by exempliﬁcation, etc.)

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are legitimate and useful. If the explanations given by the model are divorced from our ordinary explanations, what is the point of the theory? If it shows that our linguistic practices can be mapped on to a calculus, does that show that we have been operating one? Secondly, if the defender of the enterprise is willing to meet all difﬁculties by countenancing, at least in principle, exceedingly complicated rules to budget (by epicycle within epicycle) for analogy, metaphor, ﬁgurative language, idioms and the varied range of ‘semantic irregularities’ and ‘semi-productive’ operators (e.g. ‘-ness’, ‘un-’, ‘im-’), what guarantee is there that the theory will not divorce its explanations, not only from our actual explanations, but also from any possible explanation usable by us? For there is no a priori guarantee that the projected rules and transformations will be surveyable or learnable by us. They may simply be too complicated (like a proof in the notation of Principia Mathematica that 252 = 625). Is it then plausible to suppose that we actually operate such a calculus? These two objections of principle are not trivial. For what is the role of a general account of meaning if it is severed from a corresponding account of understanding? Explanations of meaning have more than one role: they explain what it is that we understand when we understand an expression; they are the content of activities (giving explanations) that constitute criteria of understanding; they are rules or standards by reference to which we judge any given use to be correct or incorrect; so they are guides to correct usage. But if the explanations given by a calculus model are divorced from our actual and possible explanations, it is difﬁcult to see what their point is. They have neither normative nor evidential roles with respect to justiﬁcation of our application of language or to our understanding. Nor do they, in any acceptable sense, replace our common-or-garden explanations. Further objections of principle can be brought. If the structure (in some fairly weighty sense) and meanings of constituents jointly determine the meaning of a sentence, it should follow that sentences with the same structure and the same constituents have the same meaning. It should also follow that structural difference should always yield difference in meaning (unless some operations cancel out). Finally, structural similarity should imply that any differences in sentence-meaning are wholly attributable to differences in constituentmeaning. But what, in this conception of the matter, is the role of the use of a sentence? Are differences of use irrelevant to meaning? Can one be said to understand what someone has said if one does not grasp what use he made of the sentence he uttered? ‘War is war’ is not typically used to afﬁrm the law of identity, and ‘Richard is himself again’ was not used to assert that Richard III had ceased to be identical with himself and subsequently came to conform to the law of identity. Context-dependent sentences show that sentences with the same structure and constituents are not necessarily used to propound the same thing. Indexicals (temporal or spatial) or pronouns do not have a different meaning from one

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occasion of use to another. The differences in the statements made by ‘This is red’, ‘He is ill’, ‘Today is my birthday’, etc. are not attributable to differences of structure or meanings of constituents, but to context (time, place, person) and use (e.g. the contrast between using ‘This is red’ to explain what ‘red’ means and using it to describe an object, and the contrast between using the same sentence to describe A, or B, or C).24 That a person understands the meaning of the constituents and the structure of the sentence does not show that he grasps what was propounded. Moreover, there are many further differences of meaning not captured by structure, content and indexicality, e.g. litotes, irony, performative uses: ‘Beethoven’s Fifth isn’t bad’; ‘Brutus is an honourable man’ said by Cassius does not have the same meaning as when said by Anthony; ‘I do’ said in response to ‘Who plays tennis?’ as opposed to ‘Do you take . . . as your wedded wife?’ differs not only because of context and speaker — it is a different kind of use.

6. Computational theories of understanding The calculus conception of language may, but need not, lend itself to compositional theories of meaning. For one may conceive of a language on the model of a calculus without thinking of the meaning (or sense) of a sentence as being composed of the meanings (or senses) of its constituents. But whether or not one cleaves to a form of compositionalism thus construed, the calculus conception is committed to the view that the meaning of a sentence in use can be derived from the meanings of its constituents. A model for such a derivation is the calculation of the value of a function for an argument from speciﬁcation of the argument and of the function. It is therefore not at all surprising that the new function-theoretic logical calculi invented at the end of the nineteenth century and duly projected on to natural languages as their hidden depth grammar should be invoked for purposes of a computational theory of understanding. For once one has succumbed to the temptation to foist a function-theoretic form of representation upon language, one will also be prone to think of knowing the meaning of a sentence (construed as understanding what is said by its use on an occasion, what ‘thought’ is expressed) on the model of knowing the answer to a calculation. Then one will be inclined to construe the question of how we can understand sentences we have never heard before on the model of the question of how we can arrive at the results of computations we have never done before. Our ﬁnal task is to show that although the later Wittgenstein does not mention the ‘problem’ of how we can understand sentences we have never 24

In MS 131, 141f., Wittgenstein remarks: ‘One has the idea that the sense of a sentence is composed of the meanings of its words. How, e.g., is the sense of “I still haven’t seen him” composed of the meanings of the words?’

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heard before, the idea that we can explained this possibility by reference to the hypothesis that we ‘calculate’ or ‘compute’ their meanings (the ‘thought’ expressed) from our knowledge of the meanings of their constituents is inimical to his later philosophy. The presuppositions of computational conceptions of understanding are as follows. (i)

(ii)

(iii) (iv)

That there is such a thing as a theory of meaning for a natural language that makes it possible to derive the meaning of any arbitrary sentence in use from the meanings of its constituent words and their mode of combination.25 That the general form of such a theory is the derivation of the truthconditions of a sentence from the meanings of its constituent words, the meaning of a word being conceived to be its contribution to the determination of the truth-conditions of any sentence in which it may occur. This is the connection between a context principle and computationalism. That speakers of a language have tacit knowledge of such a theory. That the question ‘How can one understand sentences one has never heard before?’ or ‘How is it possible to understand sentences one has never heard before?’ makes sense (and so too, presumably, that the questions ‘How can one understand a sentence?’ or ‘How is it possible to understand a sentence?’ likewise make sense).

To a ﬁrst approximation, computational theories of understanding hold that a speaker makes use of his tacit knowledge of such a theory and derives the meaning of every sentence in use that he understands from his knowledge of the meanings of their constituent words and their mode of combination in accordance with the depth grammar of the language. We have cast some doubt upon the cogency of compositionalism, upon the calculus conception of language (i.e. upon the ﬁrst presupposition), and upon the notion that the postTarskian conception of a truth-condition holds the key to the idea of meaning (the second presupposition (see further ‘Descriptions and the uses of sentences’)). But even if these are set aside, computationalism is open to further objections. The ﬁrst range of objections challenges the intelligibility of the question or questions posed (i.e. the fourth presupposition).26 ‘How can one understand sentences one has never heard before?’ and ‘How is it possible to understand sentences one has never heard before?’ are, at the very least, misleading. For they appear to ask after the means, method or manner of doing something, of performing some act or activity, or (with a Kantian transcendental ﬂourish) to ask for the pre-conditions of the possibility of doing something. There is a 25

Of course, any such theory duly budgets for indexicals and other context-dependent expressions. To be sure, there are circumstances in which one may ask ‘How could you understand that?’ or ‘How was it possible for you to understand what he said?, e.g. if it was very badly pronounced, or difﬁcult to hear in the hubbub, or in a language one did not think the hearer understood. But these are not in question here.

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presumption that there is no difﬁculty in accounting for understanding sentences one has heard before, but that there is a problem regarding sentences one has never heard before. The latter, it is tacitly implied, give rise to a special problem — the implied suggestion being that understanding sentences one has never heard before is something one does, the doing of which is, in some sense, problematic. So the question is structurally akin to asking how one executes difﬁcult tasks (e.g. starting a car without a starter key). The standard answers take it for granted that understanding such sentences is or involves some process or activity the successful execution of which has understanding as its upshot. This is immediately generalized to apply to all cases of understanding sentences. Hence the question ‘How does one understand sentences?’ supposedly makes sense too. Understanding familiar sentences equally requires that one engage in the process or activity that leads to understanding. For, it is claimed, ‘a process of derivation of some kind is involved in the understanding of a sentence’.27 The speaker’s understanding of a sentence is held to involve an instantaneous determination of its generation by the rules of the theory: ‘an adult can instantaneously determine whether (and if so how) a particular item is generated by this mechanism’.28 According to some linguists, understanding is conceived to be a state that is the product of such a process or activity. ‘What a speaker does when he understands or produces an utterance must include at least the implicit analysing of its syntactic structure . . . [and the assigning of ] interpretations to sentences on the basis of his knowledge of the meanings of their parts’.29 But, as Wittgenstein showed (see ‘Understanding and ability’, sect. 4), understanding is neither a state or experience nor an act, activity or process. To understand something said is not to do anything, and it makes no sense to ask how it is possible to do such a thing. No inner act or activity of calculation or computation is either logically necessary or sufﬁcient for understanding a given sentence. Understanding is akin to an ability, and the diffuse abilities to which it is conceptually related are those abilities exercise of which counts as satisfying the criteria of understanding. If a person understands a sentence as used by another in a speciﬁc utterance, then there are various things that person can do: he can explain what it means, can respond appropriately (with intelligence) to hearing it, can cite what is said by its use as a reason for this or that, and so forth. One might think, as Frege did, that grasping a thought must be a mental act that is performed at a given time. But this is confused. Understanding something on an occasion, or understanding something in a ﬂash, is not the performance of a mental act. Such expressions do not signify performances that take time, but rather the onset, at a time, of an array of abilities. Like winning, ﬁnding or beginning to move, understanding something 27

M. A. E. Dummett, ‘What is a Theory of Meaning?’, in Mind and Language, ed. S. Guttenplan (Clarendon Press, Oxford, 1975), p. 112. 28 N. Chomsky, ‘Review of Skinner’s Verbal Behaviour’, Language, 35 (1959), pp. 57f. 29 J. Fodor and J. J. Katz, ‘What’s Wrong with the Philosophy of Language?’, in Philosophy and Linguistics, ed. C. Lyas (Macmillan and St Martin’s Press, London, 1971), p. 282.

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on an occasion is more akin to an achievement than to a performance. Once the penny drops, then one can do the various things that manifest understanding. It is noteworthy that computational conceptions of understanding focus on the role of the hearer. But a speaker understands his own words no less than (and sometimes rather better than) the utterances of others. Can one raise the question of how a speaker understands his own words? According to the theory, a hearer, after he has heard the utterance of another, understands what was said when he, as quick as a ﬂash, interprets the words he hears, recognizes the sentential structure in which they occur, and derives the meaning of the utterance in accordance with tacitly known rules of the calculus. But when does a speaker understand his own words? Before speaking? If so, does he speak to himself ﬁrst and then interpret what he says to himself ? So he speaks to himself without understanding what he is saying to himself ! Or does he wait to see what he says aloud before he knows what it means? Or does he understand what he is saying only when he says it? — If so, then presumably he cannot know what he wants to say before he has said it. Here the picture of understanding clashes violently with its application; and this reveals the incoherence of the question in the case of the hearer too.30 For understanding a sentence is not an act, activity or process. And one does not do anything when one understands what another says, any more than one does anything in order to understand one’s own utterances. One does not normally interpret anything, and one certainly does not calculate or compute the sense of the sentence uttered, let alone ‘assign truth-conditions’ to it. That one normally knows what one wants to say before one says it means no more than that had one been asked, before one actually spoke, what one wanted to say, one could and, other things being equal, would, have answered appropriately. Since to understand the utterance of a sentence is (very roughly) to possess a cluster of abilities, it makes no sense to ask how one can understand a sentence on the model of asking how one can do something. Of course, one may ask what a person has to know in order to understand an utterance, i.e. in order to be able to do those things of which understanding consists. It is hardly news that one must know (or at least guess correctly) what the constituent words mean, and be familiar with the sentence structure.31 But that platitude gives 30

It is very striking that, faced with the question of how a speaker can produce a sentence he has never heard before, Chomsky, rather than re-examining the cogency of the question and its cousin (how a hearer can understand a sentence he has never heard before), speculates that explanation for ‘the lack of success in solving [the problem] or even presenting sensible ideas about it is that it is not within the range of human intellectual capacities: It is either “too difﬁcult”, given the nature of our capacities, or beyond their limits altogether’ (Language and Problems of Knowledge, p. 151). 31 Of course, as noted above, if a traveller to China has a phrase-book, he may know what a speciﬁc Chinese sentence means without understanding it — which is one reason why Wittgenstein remarks (somewhat hyperbolically) that to understand a sentence is to understand a language. Here one can drive a wedge between knowing what a sentence means and what is said by using it, on the one hand, and understanding it, on the other.

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no support whatsoever to the computational conception of understanding. For all it amounts to is that if one does not know what a constituent word means, the odds are that one will not understand or fully understand the utterance, and if one misconstrues the sentential structure, one is likely to misunderstand the utterance. Of course, there is a great deal more one must know, e.g. the circumstantial and discourse context of the utterance, as well as wide-ranging but humdrum knowledge of one’s fellow human beings and culture. None of this involves tacit knowledge of a calculus of meaning rules, depth grammar or logical form. Nor does possession of such knowledge as one must have imply that in understanding what one says or what another says one engages in any computational processes.32 A second range of objections questions the intelligibility of the supposed ‘tacit knowledge’ of the calculus of language. The objection is not that the notion of tacit knowledge is illegitimate. There are various forms of tacit knowledge and various things that one might mean by the phrase ‘tacit knowledge’. But it must be possible to specify what counts as tacit knowledge of a complex calculus of rules, the explicit statement of which lies beyond the powers of most speakers to grasp. There must be identiﬁable conditions that will differentiate between possession of tacit knowledge and total ignorance, conditions distinct from correct performance. For if all that shows tacit knowledge is correct performance, and all that shows lack of tacit knowledge is incorrect performance, then invoking tacit knowledge to explain how it is that someone can perform adequately is wholly empty. Furthermore, what is supposed to be tacitly known is a complex calculus of rules. These rules are supposed to guide one, since they are allegedly employed in deriving what is said by the use of a sentence one hears from the known meanings of its constituents. But a rule can guide one only if one understands it — and to understand a rule is to understand a rule-formulation, to know what it means and to know what counts as acting in accord with it. If so, then we are faced with a regress, for how can we understand the formulation of a rule that we not only have never heard before, but rather that we have never heard? It might be held that the rules that are involved are not understood at all, that they are the rules the brain follows, without understanding. But that is unintelligible. There is no such thing as the brain’s following rules — that is something that only human beings, as opposed to their brains, can do. And Wittgenstein’s extensive investigations into following rules (see Volume 2, ‘Following rules, mastery of techniques and practices’) exclude the intelligibility of the existence of rules which those who are allegedly following them never allude to or invoke, do not specify in explanations and justiﬁcations, and cannot even understand when confronted by an appropriate 32

To be sure, this does not preclude empirical investigations into the typology and regularities of misunderstanding and speech errors. What it does preclude is the idea that understanding is a process consisting in the unconscious operating of a calculus of meaning rules.

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rule-formulation. There is, Wittgenstein held, no action at a distance in grammar. But rules that are ‘deeply buried in the unconscious mind’ could act only at a distance. Rules are not causal mechanisms, and following a rule is an intentional action. A third range of objections challenges the idea that it makes sense to derive one’s understanding of a sentential utterance in one’s native tongue from one’s knowledge of what its constituent words mean and from their mode of combination.33 Wittgenstein held that the meaning of a word is its use. Words are (primarily) for use in sentences — to say something. To have mastered the technique of using words is to have acquired both the ability to employ them to say endlessly varied things by the use of sentences in which they are embedded and the various abilities constitutive of understanding what others say when they use them in sentences. Does it then make sense to know what a word means, but not to know what is said by its use in an atomic sentence34 the other words of which are familiar too? Does it make sense to know what a word means and yet to have to calculate what is thus said (by oneself or by others) in order to ﬁnd out what the atomic sentence in which it is embedded means? Is understanding a sentence really akin to knowing the result of a calculation? Is it similar to understanding the sentence ‘I have n cats and n2 + 2n − 8 = 0’, only even faster (cf. PI §513 and Exg.)? It is true that if one knows how to multiply, then one can calculate the product of 543 × 672, and in advance of the calculation one will not know the result. But can one know who N.N. is and also know what ‘is coming to dinner’ means, and not know what ‘N.N. is coming to dinner’ means without calculating anything? Can one know how to use the indexical ‘this’, know what ‘rose’ and ‘is yellow’ mean, and have to calculate what ‘This rose is yellow’ means? The arithmetical analogue of understanding the utterance of a sentence is not: knowing the answer to a calculation, such as 543 × 672 = 364,896, but rather: understanding what ‘543 × 672’ means. We were induced to think otherwise by the misguided idea that the sense of a sentence is the value of a (propositional) function for a given argument or arguments, and that the value of such a function for any given argument needs to be calculated.35 It should also be noted that the novelty of the sentence is irrelevant to the question. Linguists were induced to think that understanding new sentences is more mysterious or wonderful than understanding old and familiar sentences primarily because the relevant forms of linguistic theory evolved in reaction to behaviourist theories of language. Behaviourism, it was held, might be able 33

Although one may say this of the schoolboy poring, with dictionary and grammar book, over his Latin prose translation. 34 The qualiﬁcation ‘atomic’ is to exclude highly complex molecular sentences or sentences with multiply embedded subordinate clauses. Such cases may indeed demand a pen and paper, and some ‘calculation’. 35 For a thorough exploration of the argument sketched in this paragraph, see Eugen Fischer, Linguistic Creativity (Kluwer, Dordrecht, 2000).

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to explain, in stimulus/response terms, how we can understand old sentences, but could not possibly explain how we can understand sentences we have never heard before. But that was multiply mistaken. Behaviourism cannot adequately explain what it is to understand a familiar sentence, any more than it can adequately explain what it is to understand a novel one. And indeed, there is no greater mystery about understanding the sentence ‘The teddy is in the cot’ (which most of us have heard before) than there is about understanding the sentence ‘The teddy is in the fridge’ (which — barring its earlier occurrence in this essay — is probably novel to most readers). The criteria for understanding new sentences do not differ from the criteria for understanding old ones, and there is no reason to be amazed that someone, who asks ‘Where is Billy’s teddy?’ and is told ‘The teddy is in the fridge’, responds perfectly intelligently and with understanding by saying, ‘Why on earth is the teddy bear in the fridge?’ Finally, it should be noted that the conception of understanding that is presupposed is awry in further ways. Understanding a sentence is conceived to be a matter of deriving, from the deﬁnitions of its constituent terms and its structure, a speciﬁcation (perhaps homophonic) of its truth-conditions. We have taken issue with the idea of associating understanding with performing derivations. But it should also be observed that if all a person could do when he understood a sentence were to specify, on the basis of appropriate algorithms, that its truth-conditions are thus-and-so, we would hardly credit the person with any understanding of what was said. He would be more akin to someone deciphering a code than to someone who understood the deciphered message. The abilities constitutive of understanding an utterance are far more varied, diffuse and contextualized than the ability to specify that the sentence or proposition expressed by the sentence is true if and only if such-and-such is the case. These considerations do not purport to settle this contentious matter. They are intended primarily to demonstrate the relevance to the modern debate concerning human linguistic abilities of Wittgenstein’s reﬂections on meaning and use, on rule-following and explanations of meaning, and on understanding and ability.

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

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The standard metre 1. The rudiments of measurement Although the standard metre is mentioned only in an analogy in the Investigations §50, understanding Wittgenstein’s conception of linear measurement and the role of canonical samples in the practice of measurement has a wider importance. First, samples used to deﬁne units of measurement have a deﬁnite, formalized role in our lives. This is discussed by scientists and is roughly familiar to the well-educated. Consequently, such canonical samples provide illuminating comparisons in analysing the role of samples in less institutionalized practices. Secondly, measurement is a family-resemblance concept that raises philosophical problems. Wittgenstein stressed two: (i) Augustine’s question ‘How is it possible to measure time?’; (ii) Einstein’s question (and answer) ‘How is it possible, given the Lorentz equations, to measure simultaneity of distant events?’ (PLP 11ff.). The dissolution of such problems provides, in Wittgenstein’s view, a paradigm for the proper method of philosophizing, but it presupposes a grasp of the concept of measurement. Thirdly, measurement (especially linear) is one of Wittgenstein’s favourite sources of analogies. But these illuminate only if measuring is understood correctly. Finally, methods of measurement provide a fruitful special case to illuminate the autonomy of grammar (BT 240f.). Measuring things is a pervasive feature of our life. Learning to measure and weigh is part of elementary education. Measuring more recondite properties or measuring these properties more accurately is part of scientiﬁc evolution. The familiarity of the basic forms of measuring and the theory-laden subtleties of the advanced forms alike make an overview of measurement difﬁcult. We fail to notice the over-familiar, and we wrongly extrapolate from the over-sophisticated. The most rudimentary form of linear measurement (one might think of it as a primitive language-game) would be using an uncalibrated stick (let us call it a ‘measuring-rod’) to decide whether or not something was exactly one M long according to whether or not its ends coincide with those of the stick. If asked to explain what ‘M’ meant, each person would simply point at his own stick and say ‘That is one M’ (so there may be as many distinct concepts of length M as measuring-rod owners; but we may suppose that an Invisible Hand ensures that the measuring-rods all coincide). Introduction of calibrating

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marks and standardization of samples are natural developments from this primitive game. However, important features of measuring are present even in the rudimentary game. (i) Measuring and explaining the measure are distinct. Measuring the length of a plank is an action whose result would be formulated in a sentence (e.g. ‘This is 1 M long’) which expresses an empirical proposition and is true if the measurement was made correctly. Of course, it presupposes the meaning of the expression ‘1 M’. But someone could use the same sentence to explain what he means by ‘1 M long’. The ground for his utterance ‘This is 1 M long’, however, would not be a measurement, for he cannot lay his measuringrod alongside itself to see if it is the same length as itself. His utterance is the expression of a rule for the use of the phrase ‘1 M long’. Here the sentence is being used differently from the previous case, in which it was used to state (or describe) the length of a plank. To be sure, ‘This is 1 M long’ could be elucidated by paraphrase: ‘This rod is 1 M long’, by contrast with ‘This rod functions as my standard for the length of 1 M’, or, indeed, ‘This length (or ‘The length of this rod’) is (or ‘is to be called’ or ‘is what I call’) 1 M’. (ii) The measure (the measuring-rod) has a normative role. It has a uniform use as a standard of comparison for other objects. In the imaginary languagegame no provision is made for measuring (or calibrating) a person’s measuringrod. It is always what measures, never what is measured. Even in our more complex practice of measurement this normative role is apparent. The crucial point is that if A is being used to measure B, B cannot at the same time be used to measure A (RFM 199); i.e. nothing can simultaneously both measure and be measured against the same thing. (The normative role of instruments of measurement is built into the etymology of our general normative vocabulary: ‘norm’, ‘rule’, ‘canon’, ‘regulation’.) (iii) Description of a practice of measurement must not only deﬁne the units of measurement and the instrument, but also include speciﬁcation of admissible methods of comparing objects with instruments of measurement. Even in our primitive case we must stipulate that an object is 1 M long if its ends coincide with the ends of the measuring-rod when the two are juxtaposed. In more complex cases the background understanding is more obviously necessary. The method of juxtaposition does not explain what it means to measure the height of a mountain or the distance between two stars (‘If we imagine a series of rulers extending from one star to the other . . .’ is a bogus explanation (RFM 146f.; LFM 273f.)). For reﬁned linear measurement even the method of juxtaposition must be qualiﬁed to take account of thermal expansion and gravitational distortion. A caveat is necessary. To say that A is so-and-so many Ms long is not to describe it as having been measured in any special way. Neither statements of length nor deﬁnitions of units of measurement entail speciﬁcations of methods of comparison. But both presuppose a general practice of measuring. Indeed,

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no concept of length is independent of some practice of measuring length. Length, tautologically, is what is measured in measuring length. More perspicuously, knowing what it is to measure length is not a matter of knowing what length is and what it is to measure something (PI p. 225/191). Indeed, that misconception underlies Augustine’s puzzle about time — as if measuring a time interval must involve juxtaposition. (iv) In our simple language-game each person’s measuring-rod has a dual role, as a sample to explain his unit of measurement and as an object of comparison for measuring lengths. These two roles could be severed. We might, for example, use any rod measured to be 1 M long as a standard sample of the length 1 M. Now we would be using our measuring-rod as a ‘private’ canonical sample for generating standard samples. So in addition to conventions for methods of measuring objects we would need conventions for calibrating standard samples by reference to our canonical sample. These conventions need not coincide (e.g. in respect of thermal conditions). If a unit of measurement is deﬁned by such a (canonical) sample, this sample need not be used as a standard sample for applying the deﬁned expression. Conversely, if something is used as a standard sample in applying an expression, it need not also be used as a canonical sample in deﬁning the unit of measurement. (That depends on the practice of explaining the system.) (v) A system of measurement exempliﬁes the autonomy of grammar (see Volume 2, ‘Grammar and necessity’, sect. 7). Samples (or recipes) used to deﬁne units of measurement can be characterized as useful or useless, but there is no question of truth or falsity in their choice and no possibility of getting into conﬂict with the truth by adopting a particular deﬁnition (LFM 55f.; RFM 38f.). Using the measuring-rod to deﬁne ‘1 M’ does not depend on the rod’s being one M long. Rather we use the measuring-rod to determine the meaning of ‘1 M’, and in advance of that determination, the expression has no use. The usefulness of a choice of unit depends on us (e.g. on our size, on what kinds of instruments of measurement we use, on what measures we can manipulate), on our purposes (what kinds of things we want to measure and why), and on the normal circumstances of standard measuring. Similarly, the usefulness of the samples we use to measure depends on our purposes in making measurements, the character of the world we live in, and the materials of which the sample is made (the rigidity of rulers, the non-rigidity of tape-measures, the non-elasticity of both). In altered conditions, what we now consider useless (e.g. rulers which are elastic or have a high coefﬁcient of thermal expansion) might prove useful (LFM 83; RFM 38f., 91), and vice versa (RFM 355f., 381–3), although, of course, the samples must show a degree of reliability and predictability in the contexts in which they are used. Though the grammar of a metric of measurement is grounded in a technique of measurement, and also in the facts that make it possible and useful, such grammatical propositions as ‘12 inches = 1 foot’ do not entail descriptions of this technique and these facts (RFM 355). The deﬁnitions of units of

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measurement and principles for conversion of units have the role of rules. This is liable to be overlooked. Empirical connections may motivate adopting a rule, and the fact that cessation of certain regularities would undermine the point of having a rule may be conﬂated with the idea that the sentence expressing the rule asserts that these regularities hold (LFM 292). Illusions pile up most strongly around ‘external’ conversion principles — for example, rules for translating metric measurements into the imperial system (‘l metre = 39.37 inches’). These seem to be synthetic necessary truths, expressing real relations among the samples used to deﬁne units in unrelated systems. Properly conceived, however, these principles too are rules of grammar. They may originate in measurements, but using them as immutable conversion principles (by contrast with mutable principles for currency conversion) transforms the result of a measurement into a rule (LFM 117f.). So a metre sample can be used simultaneously as a sample of the length 39.37 inches (cf. LFM 118f.) — which is, in effect, what we do with rulers and tape-measures which are calibrated with centimetres along one side and inches along the other. They function as fragments of a conversion table, as measures for, and as samples of, two different metrics.

2. The standard metre and canonical samples The simple language-game of measuring described above is very limited. Each participant has his own standard, deﬁnes his concept of an M by reference to it alone, and measures only by applying his standard to the objects measured. Even if an Invisible Hand ensured the coincidence of all measuring-rods, assiduous tampering (like clipping of coinage) could disrupt the pre-established harmony. For the game to have a serious point in a society that engages in transactions involving measurement, it must be standardized and institutionalized. The obvious remedy is to establish an object (e.g. the monarch’s measuringrod) as the authoritative (canonical) sample of a certain length. This was the role of the Standard Metre Bar originally kept in the Louvre (or the Imperial Bar at Greenwich). Introducing a canonical sample typically will not affect people’s use of their measuring-rods both to measure and to give ostensive explanations of the meaning of ‘1 M’. But it will, in our imaginary languagegame, render ‘1 M’ a shared concept. It will establish a criterion of correctness for ostensive deﬁnitions given by people by reference to their measuring-rods. No longer is each person’s measuring-rod something he never measures but always uses to measure; now he may measure his rod against the canonical sample to judge its correctness as a standard sample. Now his ostensive deﬁnition by reference to his rod is correct only if his rod coincides in length with the canonical sample. Equally, his judgement that A is 1 M long turns not only on A’s coincidence in length with his measuring-rod, but also on whether his rod coincides in length with the canonical M. Thus canonical

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samples standardize common measuring instruments and provide a court of ﬁnal appeal for resolving disagreements in deﬁnition and judgement. The canonical M, however, is never something measured, but always what measures (typically, but not necessarily exclusively, it measures — calibrates — standard measuring-rods in general use). It is important neither to exaggerate nor to underestimate the function of a canonical sample like the Standard Metre Bar. We are prone to exaggerate its role if we think that ‘One metre = df the length of the Standard Metre Bar’ is the only adequate deﬁnition of the term. This is an illusion. Giving this deﬁnition is one criterion of understanding the term. Giving an ostensive deﬁnition is another. Giving the former explanation no more guarantees understanding than giving the latter. Giving either kind of deﬁnition may fail to establish understanding if the person does not know how to apply the expression correctly. This illustrates two points. First, there may be multiple correct explanations for a given term. Secondly, explanations do not apply themselves, hence giving a correct explanation does not guarantee ability to use the deﬁned term correctly; hence it is only a criterion, not a sufﬁcient condition of understanding. We may equally underestimate the signiﬁcance of the Standard Metre Bar. Most people who participate in the practice of metric measurements are ignorant of its role, indeed, even of its existence, and yet may correctly measure quite unproblematically. This makes it appear as if the function of the Standard Metre Bar is an instance of ‘action at a distance’, i.e. something that drops out of a description of what is understood in understanding the system of measurement. This is illusory: the institution of metric measurement includes aspects of which the ordinary man is ignorant — e.g. procedures for calibrating standard samples. He knows what the expression ‘one metre’ means. He can apply it correctly, measure things with his rulers or tapemeasures, and explain what it means by reference to them. But he has only a partial understanding of the whole institution of metric measurement, although that is sufﬁcient for his purposes.

3. Fixing the reference or explaining the meaning? If samples, which are objects with a special use, belong to our method of representation, then does not their vulnerability to fortune place logic, the determination of sense, at the mercy of the facts? While introducing canonical samples enables us to check the standard samples used in applying the term for which they are samples, it seems to put all our eggs in one basket. Would not damage or destruction of the Standard Metre Bar affect our practices of measurement? There are two actual remedies to this threat. (i) We might multiply authoritative samples, giving each equal status, and preserve them in different places.

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(ii) More sophisticatedly, for reﬁned scientiﬁc purposes, we may replace canonical samples by canonical recipes involving natural constants that can readily be replicated in laboratories (e.g. ‘1 metre = df 1,650,763.73 wavelengths of the light in the spectrum of the krypton-86 atom in a vacuum’ was the deﬁnition adopted in 1960 by the International Bureau of Weights and Measures, which was, in its turn, replaced in 1983 by the deﬁnition ‘1 metre = the distance travelled by light in a vacuum in 1/299,792,458 of a second’). This protects the system of measurement from annihilation, since a canonical recipe is not vulnerable to accidental destruction through ﬁre or earthquake, and facilitates international consensus on standards of measurement. Looked at askew, it may appear as if the grammar of measurement is in the lap of the gods. After all, the canonical measuring-rod may expand or contract, be bent or burnt. One may grant that in a sense, any system of measurement must be at the mercy of samples. In the simple language-game with measuringrods, each person is at the mercy of his own measuring-rod. Introducing canonical samples or recipes does not change vulnerability to general facts of nature. Unless every deﬁnition of a certain length (such as one metre) were subject to a yet higher court of appeal, the system of measurement that invokes samples or recipes for their production must at some point be at the mercy of fate. But, in a qualiﬁed sense, our fate is in our hands. For objects are used as samples only on our sufferance; i.e. their status as samples is up to us. We may change the use of a sample or cease to use a given object as a sample at all. (This change might be motivated by a shift in our purposes or a reﬁnement in methods for comparing objects with samples.) The Standard Metre Bar, as noted above, has been demoted from its former status as the canonical sample of the length one metre (and replaced by a canonical recipe), but not because it has suffered any damage. Samples are, in this sense, creatures of our will. ‘One metre = df the length of the Standard Metre Bar’ obviously does not mean that one metre is the length of the Standard Metre Bar whatever that may be. That would be absurd, since we would then have to surrender to whatever we found in Paris (which, if stretched, might be the length of a telephone pole). Rather, it was stipulated that one metre is the length that the Standard Metre Bar has under certain speciﬁed conditions (of temperature, etc.), just as one gram is stipulated to be the mass of a cubic centimetre of pure water under certain speciﬁed conditions (namely, at sea-level at maximal density (4° centigrade)).1 But now we are not at the mercy of the sample in the same way. If the bar were heated or stretched, it would not then have the length it now has, and the conditions under which we choose to use it as a sample would not be satisﬁed. In short, we used the Standard Metre Bar as a canonical sample, but we could cease to do so if we wished (and in fact we have done so). So the thought that the Standard Metre Bar might, in some other ‘possible world’, 1

Measurements of a volume of water being imprecise and difﬁcult to make with the desired accuracy, the canonical sample for 1 kilogramme is a platinum-iridium cylinder at Sèvres.

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have been longer or shorter under such-and-such conditions than it is in this world is irrelevant to understanding our practice. The meaning of ‘one metre’ depends on how we do use samples, not on how we might (or might not) use them in different conditions. It may seem that the proper way to respond to the fear that we are at the mercy of the facts is to deny that the sentence ‘One metre is the length of the Standard Metre Bar’ is anything other than a contingent truth. What is at the mercy of the facts is that this particular platinum-iridium bar is one metre long. It might have been longer or shorter, and may become longer or shorter — but the length one metre is perfectly secure from the predations of Fortune. The Standard Metre Bar is not a sample, but an example — an example of a certain length that we pick out by reference to this metal bar. The Standard Metre Length, like all Platonic Objects, is safe enough — the only problem is identifying it. So, it has been objected that Wittgenstein’s remark (PI §50) that the Standard Metre Bar in Paris is neither a metre long nor not a metre long is mistaken. Indeed, his remark, contrary to what he says, does ascribe to this platinum-iridium bar a quite ‘extraordinary property’, indeed an incoherent one.2 It is surely a contingent truth that this metal bar is the length it is. And if it is a contingent truth, then it is a truth. So the Standard Metre Bar is one metre long. Again, the Standard Metre Bar is 39.37 inches long. An object that is 39.37 inches long is a metre long. So the Standard Metre Bar is surely a metre long! Finally, the deﬁnition ‘1 metre = df the length of the Standard Metre Bar’ does not give the meaning of ‘1 metre’ but rather ﬁxes its reference; i.e. it picks out a certain length which, as a matter of contingent fact, this metal rod has.3 So the Standard Metre Bar is that length! This reasoning is confused. Wittgenstein noted in §50 that saying that the Standard Metre Bar is neither a metre long nor not a metre long is not attributing to it an extraordinary property at all, but merely marks its role in the language-game of measuring with a metre rule. Close attention to this thought will enable one to see through the fog. (i) The Metre Bar is a sample. The sample is not the length of the metal rod, it is the rod itself (PR 81). What we measure and calibrate with is, after all, the metal bar (and not faux de mieux either, as if the length without a rod would be the Ideal Platonic Measure). To say that it is a sample is to say that it belongs to our means of representation, and is not something represented (PI §50). So we must view it as something that is used in representing how other things are. 2

S. Kripke, Naming and Necessity (Harvard University Press, Cambridge, Mass., 1980), pp. 54f. It is, Kripke averred, marked out ‘by an accidental property, namely that there is a stick of that length. Someone else might mark out the same reference by another accidental property’ (ibid., p. 55). The accidental property is a ‘property’ of the length one metre: namely, the property of being had by the Metre Bar. But one might also mark it out by reference to the different accidental property of being had by the piece of string in one’s pocket. 3

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(ii) The sentence ‘One metre is the length of the Metre Bar’ is not the result of a measurement (of an experiment, as it were). It is not a contingent identity-statement ﬂanked by a name on the left and a deﬁnite description on the right, stating that the length one metre has been discovered to be the length of a certain metal bar (as Jack might be discovered to be the husband of Jill). It is rather a deﬁnition (and was originally a stipulation). It is used here to state a rule: namely, that any object can be said to be one metre long if it is the length of the Metre Bar. (iii) ‘One metre is the length of the Metre Bar’, used to express a rule for the use of the phrase ‘one metre’, is no more a contingent truth than ‘The chess king moves one square at a time’. We could play a game in which the king moves three squares at a time — but then it would not be chess but a different game. Similarly, we could have chosen a longer or shorter paradigm to deﬁne our unit of measurement, but had we done so, the unit would not have been what we now call ‘a metre’. If ‘One metre is the length of the Metre Bar’ is not a contingent truth, is it then a necessary truth? Is it a necessary truth that the chess king moves one square at a time? We need to be much clearer about the nature of the various things that have been called, and that we are naturally inclined to call, ‘necessary truths’ before we can fruitfully pose that question in order to dissolve a particular philosophical puzzlement (for discussion of Wittgenstein’s reﬂections on necessary truths, see Volume 2, ‘Grammar and necessity’). The question needlessly multiplies confusion at this stage. The better question to ask is: What is the role of this sentence? What do we use it for? What is its function in the language-game with metric measurement? The role of this sentence is not to describe how things are, but to present a norm of representation. But surely, one might object, we can say that it is true that the length of the Standard Metre Bar is one metre? And if it is true, then is it not a statement of fact? We can indeed say that it is true. But the truth-operator is notoriously polygamous, and the moot question is what the truth-ascription amounts to. We can say that it is true that the king in chess moves one square at a time, but that does not make the assertion that the chess king moves one square at a time any the less a statement of a rule of chess. In both cases, all the truth-operation does is to reafﬁrm a rule. (iv) It is perfectly correct that we can say that the Standard Metre Bar is 39.37 inches long. It is also true that 39.37 inches = 1 metre. But it does not follow that, as a matter of fact, the Standard Metre Bar is a metre long. For ‘39.37 inches = 1 metre’ is a conversion principle, a rule, not the result of a measurement (or ‘an experiment’ as Wittgenstein calls it), although one might say that it is the result of a measurement’s (an experiment’s) being hardened into a rule. What does follow is that the Standard Metre Bar can be used both as the canonical sample for a metre length and as a canonical sample for being 39.37 inches long. (v) Does ‘One metre is the length of the Metre Bar’ merely ﬁx the reference of the phrase ‘one metre’, namely a certain length, by selecting an object,

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namely the Standard Metre Bar, that contingently (‘accidentally’) has this property? Not so. It is at best confused to suggest that it is a property of the length one metre that such-and-such a metal bar ‘has it’. P may be a property of substance S, but being had by S is not a relational property of the property P (unlike the genuine relational property of being owned by S, which is a property of S’s chattels). For ‘being had by’, thus used, does not signify a relation at all.4 The explanation ‘One metre is the length of the Standard Metre Bar’ is not a reference-ﬁxing description like ‘Jack is the husband of Jill’. It is not a description at all, and it does not pick out one metre by reference to a contingently identifying property which that length has. It gives the meaning of the phrase ‘one metre’, just as the ostensive deﬁnition ‘This colour + n is black’ gives the meaning of the word ‘black’. Indeed, instead of saying ‘This table is one metre long’, one can say ‘This table is the length of the Standard Metre Bar’ (which is not a nonsensical identity-statement, but a true or false predication). This is parallel to the fact that instead of saying ‘The ﬂoor is black’, one can say ‘The ﬂoor is this colour + n’.

4. Defusing paradoxes To use sentences such as ‘This is one metre’, ‘This length is one metre’, ‘The length of this rod is one metre’ to explain the term ‘one metre’ is not to describe the rod. The ostended rod is being used on this occasion as a sample, not as something described; this is independent of whether the sample is canonical, standard or optional. A piece of string a metre long can, on one occasion, be used as a sample (an optional sample) in an ostensive explanation, but on another it can be described by the (genuine) proposition ‘This is one metre long’. In our primitive measuring game each participant deﬁned ‘1 M’ solely by reference to his own measuring-rod; i.e. it was the sample for explaining his unit of measurement. Here the use of ‘This is 1 M long’ said when pointing at one’s own stick cannot but be grammatical. It is an explanation of what ‘1 M’ means, not a description of how long the stick is. So it gives a rule for the use of the expression ‘1 M’: namely, that anything can be said to be one M long if it is the length of this + measuring-rod. Hence, in this language-game, there is, relative to each player, one thing of which he cannot say that it is, or is not, 1 M long, i.e. which he cannot describe thus. But relative to the whole group, there is nothing with this privileged status, since nothing is used as a community-wide sample for a shared concept of an M. Our Standard (canonical) Metre Bar plays (or played) a role relative to everyone that parallels the role played in the primitive game by each person’s 4 ‘A has the length of one metre’ does not signify a relation between A and the length one metre, but is just a clumsy way of saying that A is a metre long. Hence one cannot transform ‘A has the length of one metre’ into ‘The length of one metre has the property of being had by A’, whereas ‘A owns (has) this house’ can be transformed into ‘This house has the property of being owned by A’.

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measuring-rod relative to himself alone. Hence in our practice there is indeed one thing that cannot be said to be or not to be one metre long: namely, the Standard Metre Bar. Claiming that the Standard Metre Bar cannot be described as being or not being one metre long is indeed not to attribute to it an extraordinary metaphysical property. It simply expresses the special role that a certain platinum-iridium bar has (or had) in the institution of linear metric measurement. The only impossibility lies in simultaneously using the Standard Metre Bar as a canonical sample that is used to deﬁne the expression ‘one metre’ and describing it as measuring one metre in length. There is no such thing as something which always measures and is never measured, but which is also sometimes measured and found to be one metre long. Consider the following pattern of argument: Y is the same length as X. The length of X is one metre. ∴ the length of Y is one metre.

If ‘X’ is replaced by ‘the Standard Metre Bar’, then the second premiss drops out, and the inference is immediate. This is evident, since the Standard Metre Bar is used to deﬁne the length ‘one metre’. If an object coincides in length with the Standard Metre Bar, then it is one metre in length, since we use that metal bar to deﬁne the length ‘one metre’. But this may seem to generate a paradox. For how can this metal bar be said to be neither a metre long nor not a metre long? Surely it cannot have a length that is neither the same as nor different from one metre! Does that mean that it does not have a length? — But that is absurd. First, as is evident from the above pattern of argument, if it had no length, then nothing could be described as being (or not being) one metre long, because to say that X is one metre long is to say that X is the length of the Standard Metre Bar. Secondly, every rod has a length; a fortiori, the rod we denominate ‘the Standard Metre Bar’ has a length. Thirdly, might we not measure the Standard Metre Bar with a trusty foot-rule and discover its length to be 39.37 inches? Since it can be said to have a non-metric length, it can be said to have a length tout court. We seem to face the Antinomy of the Standard Metre. This paradox arises from our looking askew at the use of samples and the use of the sentence incorporating the predicate ‘has a length’. ‘Every rod has a length’ is a grammatical proposition (PI §251). It signiﬁes that if anything can be said to be a rod, it can also be said to have a length. There is no such thing as a rod without a length. But the Standard Metre Bar is a rod. So it has a length. Obviously, we can licitly say that the standard metre bar is 39.37 inches long. But that is just to gesture at a conversion rule. The point is that the Standard Metre Bar determines what it is to be one metre long, and therefore cannot itself be said to be one metre long — there is no such thing as using a standard of measurement to measure itself. The statement that X is the length

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of the Standard Metre Bar says no more than that X is one metre long, since ‘the length of the Standard Metre Bar = df 1 metre’. But to say that the Standard Metre Bar is one metre long is to say that the Standard Metre Bar is the length of the Standard Metre Bar, i.e. to say nothing at all. And to deny that it is one metre long is to deny that it has the length it has, i.e. to talk nonsense. So, there is one thing of which one can say neither that it is one metre long, nor that it is not one metre long (cf. PI §50). This does not mean that it does not have a length. It means that we use its length as a standard, and determine by reference to it the unit of measurement we use to measure other things.

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

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Family resemblance 1. Background: deﬁnition, logical constituents and analysis The temptation to think that a concept applies to the various things that fall under it in virtue of those things’ possessing common properties is as old as philosophy. Socrates, in the early Platonic dialogues, investigating the virtues, explained that what he demanded of an answer to such questions as ‘What is piety?’ was an explanation of the essence of piety, i.e. of what makes all pious things pious or in virtue of what pious things are pious (cf. Euthyphro 6d). In the Cratylus (388c), Plato argued that ‘a name is an instrument of teaching and of distinguishing natures’. The quest for a deﬁnition of F, as he conceived it, was an investigation into the essential nature of F-ness, not a lexicographical inquiry. What it is to be F is deﬁned by specifying the Form common to all things that are F. The Form of F, he thought, consists in pure F-ness, unadulterated by admixture. But all things that are F ‘participate’ to a greater or lesser degree in the Form of F, have F as an adulterated ingredient in their constitution. A conception of deﬁnition as an investigation into essences was also enshrined in Aristotle’s methodology, although he rejected the Platonic notion of Forms. The proper deﬁnition of a substance according to Aristotle will state its genus and speciﬁc differentia — for that describes its essence. Accordingly, a correct deﬁnition is a true proposition concerning the entity deﬁned. Deﬁnition, thus conceived, became known as ‘real deﬁnition (deﬁnitio rei)’, i.e. deﬁnition of things, and was contrasted with mere ‘nominal deﬁnition (deﬁnitio nominis)’, i.e. deﬁnition of names. The conception informed much scholastic thought and survived well into the early modern era. The Port-Royal Logic (1662) characterized real deﬁnition as identifying the nature of a thing by identifying its essential characteristics.1 This was to be done either by speciﬁcation of genus and differentia or by enumerating ‘integral parts’ (e.g. ‘man is a composite of mind and body’). A requirement on a real deﬁnition is that it ‘enable us to understand the nature of any referent of the deﬁned word sufﬁciently to account for the referent’s principal characteristics’ (ibid.). Nominal deﬁnitions, by

1

A. Arnauld, The Art of Thinking: The Port Royal Logic (Bobbs-Merrill, Indianapolis, 1964), Pt II, ch. 16.

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contrast, were conceived to be either stipulations (which cannot be disputed) or descriptions of common usage (which are no more than factual records concerning speech habits). Spinoza, writing at much the same time as Arnauld, held that ‘a deﬁnition, if it is to be perfect, must explain the inmost essence of a thing’.2 And Leibniz, opposing Hobbes’s nominalism, accepted a version of the distinction between real and nominal deﬁnition, holding that real deﬁnitions, by contrast with stipulative ones, are non-arbitrary, and enable us to demonstrate the possibility of things.3 A conception of analysis informed the philosophical methodology of many early modern philosophers, irrespective of whether they accepted an essentialist conception of deﬁnition. The Port-Royal idea of analysis was derived from Descartes.4 Arnauld distinguished between analysis, or the method of resolution, and synthesis, or the method of instruction, both being ways of arranging sequences of propositions, the former with a view to discovering new truths (or displaying the order of their discovery), the latter with a view to instructing learners in what is known. The approval of analysis thus conceived and the denigration of synthesis (which included the deductive presentation of arguments) was an aspect of the Cartesian elevation of epistemology over logic. A century later Condillac, in his Essay on the Origin of Human Knowledge (1746) was still denigrating the method of synthesis with its allegedly futile appeal to principles and deﬁnitions.5 Nevertheless, it is not surprising that the conception of real deﬁnition was harnessed to that of analysis. Isaac Watts, in his Logick (1744), taking the conception of method from the Port-Royal Logic, remarked that the ‘Analytic method takes the whole Compound as it ﬁnds it, whether it be Species or an Individual, and leads us into the Knowledge of it by resolving it into its ﬁrst Principles or Parts, its generic Nature and its special Properties; and therefore it is called the Method of Resolution’.6 Analysis, he further explains, ‘ﬁnds out the general and special nature of a Thing by considering 2 Spinoza, Improvement of the Understanding, I. 31, in The Chief works of Benedict de Spinoza, tr. R. H. M. Elwes (Dover, New York, 1955), vol. 2. 3 Leibniz, ‘Reﬂections on Knowledge, Truth and Ideas’ (1684), tr. and repr. in P. P. Weiner, Leibniz: Selections (Scribner’s, New York, 1951), p. 287. By contrast, Locke held that ‘a Deﬁnition is nothing else but the shewing the meaning of one Word by several other not synonymous Terms. The meaning of Words, being only the Ideas they are made to stand for by him that uses them; the meaning of any Term is then shewed, or the Word is deﬁned when by other Words, the Idea it is made the Sign of, and annexed to in the Mind of the Speaker, is as it were represented, or set before the view of another; and thus its Signiﬁcation ascertained: This is the only use and end of Deﬁnitions’ (Essay Concerning Human Understanding, Bk III, ch. IV, sect. 6.) The knowledge of ‘real essences’ of substances that is demanded by proponents of real deﬁnitions would be knowledge of the corpuscularian structure of things that is not available to us. 4 Analysis, according to Descartes, ‘shows the true way by means of which the thing in question was discovered methodically’ (‘Replies to the 2nd Objections’). 5 Condillac, Essay on the Origin of Human Knowledge, ed. and tr. Hans Aarsleff (Cambridge University Press, Cambridge, 2001), I. 2–7. 6 Isaac Watts, Logick: or The Right Use of Reason, 2nd edn (London, 1726), Pt IV, ch. 1 (p. 341).

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the various Attributes of the Individuals, and observing what is common, and what is proper, what is accidental and what is essential’.7 Commitment to a distinction between real and nominal deﬁnition lasted into the nineteenth century. It was ﬁercely attacked by Mill in A System of Logic (1843) in his criticisms of Whately’s Logic.8 He insisted (following Locke) that a deﬁnition ‘is a mere identical proposition, which gives information only about the use of language, and from which no conclusions affecting matters of fact can possibly be drawn’,9 and argued that no deﬁnition could ever ‘unfold the nature of a thing’ in the sense intended by defenders of the notion of real deﬁnition.10 Thereafter, for more than a century, few sprang to defend the idea under its ofﬁcial name. But the founding fathers of analytic philosophy were, in important respects, committed to a very similar conception of deﬁnition in philosophy. Frege investigated the question ‘What is a number?’ in The Foundations of Arithmetic (1884). He held it to be ‘a scandal that our science [arithmetic] should be so unclear about the ﬁrst and foremost of its objects’ (FA p. ii). What he pursued was a deﬁnition of the concept of number, acknowledging that ‘Often it is only after immense intellectual effort, which may have continued over centuries, that humanity at last succeeds in achieving knowledge of a concept in its pure form’ (FA p. vii). This quest was patently conceived to be for the essence of number, a matter of neither lexicography nor stipulation, but of discovery. Deﬁnition, he held, is logical analysis (logische Zerlegung (FC 147 (18)), and Frege demanded of the deﬁnition of a concept that it specify the necessary and sufﬁcient conditions for its application.11 He conceived of logical analysis as akin to chemical analysis: ‘The mental activities leading to the formulation of a deﬁnition may be of two kinds: analytic or synthetic. This is similar to the activities of the chemist, who either analyses a given substance into its elements or lets given elements combine to form a 7 Ibid., p. 344. Watts gives as an example ﬁnding that ‘by surveying the Colour, the Shape, Motion, Rest, Place, Solidity, Extension of Bodies, we come to ﬁnd that the Nature of Body in general is Solid Extension; because all other Qualities of Bodies are changeable, but this belongs to all Bodies, and it endures thro’ all Changes’. 8 Precursors in rejecting real deﬁnition among the British empiricists were Hobbes, Locke and Reid. Reid observed that ‘A deﬁnition is nothing else but an explication of the meaning of a word, by words whose meaning is already known’ (Essays on the Intellectual Powers of Man, critical edn, ed. Derek R. Brookes (Edinburgh University Press, Edinburgh, 2002), I, 1). Nevertheless, he accepted the view that deﬁnable expressions were deﬁned by genus and differentia, and held that expressions not thus deﬁnable signify things that are simple ‘and void of all composition’. These we must endeavour to explain as best we can, but they are not susceptible to ‘logical deﬁnition’. 9 J. S. Mill, A System of Logic: Ratiocinative and Inductive, in Collected Works of John Stuart Mill, vol. 7 (University of Toronto Press, Toronto, 1973), I, viii, §5. 10 The Kneales assert that ‘After Mill’s book little was heard of the doctrine of real deﬁnition’ (W. and M. Kneale, The Development of Logic (Clarendon Press, Oxford, 1962), p. 374.) 11 He focused upon deﬁnition in terms of characteristic marks (Merkmal deﬁnition), but recognized and utilized other forms of analytic deﬁnition. For present purposes these may be disregarded.

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new substance’ (FG I, 302 (303)). Analysis discloses the characteristic marks that ‘make up’ a concept, that are ‘component characteristics’ (FA §53) or ‘logical parts’ (logische Teile (FG I 283 (373))) of the concept, while being at the same time properties of whatever falls under the concept. The logician cannot ‘require that everything shall be deﬁned, any more than one can require that a chemist shall decompose every substance. What is simple cannot be decomposed, and what is logically simple does not admit of analysis and accordingly cannot have a proper deﬁnition (FC 147 (18)). ‘Now something logically simple is no more given us at the outset than most of the chemical elements are; it is reached only by means of scientiﬁc work’ (CO 182 (193)). How are these ‘discoveries’ about the essences of things related to our ordinary understanding of the expressions involved? After all, mankind has been using number-words since time immemorial, without knowing that numbers are classes of classes. On this matter Frege had little to say, save to remark that through the quest for a deﬁnition ‘one becomes more and more clearly aware of the content of what one has connected, albeit only half consciously, with a certain word’ (FG I 274 (320), n. 4). The chemical analogy was tempting. Chemical analysis terminates in elements (or atoms) that cannot be further chemically decomposed, and similarly, logical analysis seems to terminate in the elements (or atoms) of thought and language that are unanalysable and indeﬁnable — the simple natures of Descartes, the simple ideas of the empiricists, or simple and unanalysable concepts. Just as we know that objects are compounded out of chemical elements, so too, it may seem, we know that thought must be compounded out of the basic building-blocks of simple ideas or concepts. Just as chemical analysis yields elements out of which all stuffs and all things are compounded, so too, it seems, logical analysis reveals both the constituents of concepts or ideas and the ingredients of particulars or individuals (e.g. the property of rigidity is both a logical part of the concept of a beam and an ingredient of any object that is a beam). Thinking along these well-worn tracks, it seems that the search for deﬁnitions is the search for those ingredients of everything falling under a given concept F that makes them Fs. So analysis must terminate in names of such pure elements of which things logically consist. The demand for analytic deﬁnitions specifying characteristic marks of a concept must be distinguished from the even more stringent demand for ‘completeness of deﬁnition’ or determinacy of sense. This too was required by Frege. Concepts, he argued, ‘must have a sharp boundary’. All vagueness must be eliminated. It must be absolutely determinate for any object whether it falls under any given concept or not. ‘A concept that is not sharply deﬁned is wrongly termed a concept. Such quasi-conceptual constructions cannot be recognized as concepts by logic; it is impossible to lay down laws for them. The law of excluded middle is really just another form of the requirement that a concept should have a sharp boundary’ (BLA ii §56). Not only must any concept-word be circumscribed by a closed boundary speciﬁed by its characteristic marks,

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but further, the boundary must be ‘sharp’, excluding any borderline cases in all possible circumstances.12 While Frege was a precursor of modern analytic philosophy, its founding fathers were Moore and Russell, and it is remarkable to see the extent to which they too were enmeshed in webs woven more than two millennia earlier. Moore, in Principia Ethica (1903), raised the question of how good is to be deﬁned. A verbal deﬁnition, he averred, is of mere lexicographical interest — it is either an arbitrary stipulation or a description of usage. But a philosophical deﬁnition of something is concerned ‘solely with the object or idea . . . that the word is generally used to stand for. What I want to discover’, he wrote, ‘is the nature of that object or idea.’ Deﬁnitions of the kind he was seeking, ‘deﬁnitions which describe the real nature of the object or notion denoted by a word, and which do not merely tell us what the word is used to mean, are only possible when the object or notion in question is something complex. . . . The most important sense of “deﬁnition” is that in which a deﬁnition states that there are parts which invariably compose a certain whole.’13 Russell had a similar conception. Deﬁnition, in philosophy, is the analysis of an idea into constituent ideas (PrM 27). It is ‘the discovery of the constituents and the manner of combination of a given complex’ (TK 119); ‘true analysis . . . must be reached, like a scientiﬁc hypothesis, as the theoretic residue left by the comparison of data’ (TK 33). Rebelling against the Hegelianism of his youth, Russell averred that the essence of philosophy ‘is analysis not synthesis’.14 Analysis may well come up with wholly unanticipated results, genuine discoveries about the underlying natures of things. Frege, Russell pointed out, deﬁnes the number 2, for instance, as the class of all couples, and the number three as the class of all triads. This does not seem to be what we have hitherto been meaning when we spoke of 2 and 3, though it would have been difﬁcult to say what we have been meaning. The answer to a feeling cannot be a logical argument, but nevertheless the answer in this case is not without importance. In the ﬁrst place, it will be found that when an idea which has grown familiar as an unanalysed whole is ﬁrst resolved accurately into its component parts — which is what we do when we deﬁne it — there is almost always a feeling of unfamiliarity produced by the analysis, which tends to cause protest against the deﬁnition. . . . the real desideratum about such a deﬁnition as that of number is not that it should represent as nearly as possible the ideas of those who have not gone through the analysis required in order to reach a deﬁnition, but that it should give us objects having the requisite properties. (OK 204f.)

12

The motivation for this impossible demand was Frege’s assimilation of concepts to functions. For a function, he held, is fully speciﬁed only if its value for any possible argument can be determined. 13 G. E. Moore, Principia Ethica (Cambridge University Press, Cambridge, 1960), p. 7. 14 Russell, ‘On Scientiﬁc Method in Philosophy’ (1914), repr. in The Collected Papers of Bertrand Russell, vol. 8 (Allen and Unwin, London, 1986), p. 66.

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So, we may well all have been using a certain expression, say ‘two’ or ‘justice’, all our lives without having any clear idea, let alone a distinct idea, of what it signiﬁes. The ‘logical-analytic method’ in philosophy, he wrote, citing Frege as its originator, is ‘something completely deﬁnite, capable of being embodied in maxims, and adequate, in all branches of philosophy, to yield whatever objective scientiﬁc knowledge it is possible to obtain’ (OK p. v). And the knowledge it yields, Russell thought, is knowledge of the natures of things. The Tractatus followed in the footsteps of Frege and Russell. Names of complexes are analysable by a variant of Russell’s Theory of Descriptions. Complex concept-words are analysable into their characteristic marks. The ﬁnal residue of analysis consists in the simple names, the meanings of which are simple objects that constitute the substance of the world. These names are concatenated into elementary propositions that are bipolar and logically independent. They divide logical space precisely into two. Indeed, the demand for simple names is a form of the demand for determinacy of sense (TLP 3.23). Any apparent vagueness in the surface grammar of propositions will disappear on analysis, which will reveal that all indeterminacy is determinately indeterminate, since it consists of disjunctions of sharply determined possibilities (cf. NB 61, 63). The simple names are the foundations of language and the points at which it is connected with the world. So analysis simultaneously reveals the nature of language and the essence of the world (NB 79). Philosophy seemed a sublime investigation that strives to see through phenomena to discover their essential, metaphysically determined, possibilities (cf. PI §89; the Leibnizian afﬁnity is striking). Common to this essentialist, Platonic tradition was the thought that everything to which an unequivocal word applies must have common properties.15 The essentialist conception simply insists that a word that does not satisfy this requirement is not a genuine concept-word, but is polysemic. If it further demands elimination of any possible vagueness, then a word that is not so deﬁned as to ensure that every possible object in any possible circumstance either clearly falls under the concept or does not is likewise not a genuine concept-word. As noted, a corollary of this Platonist conception was that in order to have mastered the use of a concept-word, it is not necessary to know its analysis or the common properties of things in its extension. This ought to have occasioned more qualms. For if we argue thus, then we either sever understanding from the ability to say (explain) what we understand, or we do not understand what we are saying. Have we all been using number-words, for example, without understanding them? Or do we understand them without knowing what 15

Of course, equivocal terms require multiple deﬁnitions for disambiguation. The Port-Royal Logic had distinguished among equivocals between plain polysemy (e.g. ‘canon’) and analogues, e.g. ‘health’ as applied to animals, food, exercise, air, etc. (the example is Aristotle’s). In such cases two ideas are connected by relations of cause, effect, sign or similarity between what they are ideas of (ibid., pp. 50f.). Here the analogues radiate outwards, as it were, from a common centre.

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they really mean? Or do we have ‘tacit knowledge’ of what they mean? (And how does that differ from ignorance?) However, some philosophers paid less homage to the Platonic essentialist tradition and recognized the fact that many words do not signify common properties that anything falling under the concept must possess, and yet are useful for all that. Dugald Stewart, writing in 1810, criticized the prejudice in favour of deﬁnition by genus and differentia, which, he averred, has led to distortions in philosophical investigations of causation, goodness, beauty, etc. ‘Suppose’, he wrote, that the letters A, B, C, D, E, denote a series of objects; that A possesses some one quality in common with B; B a quality in common with C; C a quality in common with D; D a quality in common with E; while at the same time, no quality can be found which belongs in common to any three objects in the series. Is it not conceivable, that the afﬁnity between A and B may produce a transference of the name of the ﬁrst to the second; and that, in consequence of the other afﬁnities which connect the remaining objects together, the same name may pass in succession from B to C; from C to D; and from D to E? In this manner, a common appellation will arise between A and E, although the two objects may, in their nature and properties, be so widely distant from each other, that no stretch of imagination can conceive how the thoughts were led from the former to the latter. The transitions, nevertheless, may have been so easy and gradual, that were they successfully detected by the fortunate ingenuity of a theorist, we should instantly recognise, not only the verisimilitude, but the truth of the conjecture.16

Different conclusions can be drawn from such observations. One might conclude, as Frege would have done, that such expressions are hopelessly polysemic and altogether unﬁt for science and logical reasoning. So Mill remarked that a name not infrequently passes by successive links of resemblance from one object to another, until it becomes applied to things having nothing in common with the ﬁrst things to which the name was given; so that it at last denotes a confused huddle of objects, having nothing whatever in common; and connotes nothing, not even a vague and general resemblance. When a name has fallen into this state, in which by predicating it of any object we assert literally nothing about the object, it has become unﬁt for the purposes of either thought or of the communication of thought.17

And Bain, noting the way in which superﬁcial similarities thus incline us to extend terms in an arbitrary and irregular fashion, remarked that the result is all too often a term ‘wholly unﬁt for accurate reasoning’, and that the ‘methods 16

Dugald Stewart, Philosophical Essays (Creech and Constable, Edinburgh, 1810), p. 218. Mill, System of Logic, I, viii, §7. Mill gave as an example of this ‘natural degeneracy of language’ the much discussed term ‘beautiful’: ‘it is impossible to give the word Beautiful any ﬁxed connotation, such that it denote all the objects which in common use it now denotes, but no others. A ﬁxed connotation, however, it ought to have: for, so long as it has not, it is unﬁt to be used as a scientiﬁc term’ (IV, iv, §5).

17

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of deﬁnition are bafﬂed for want of sufﬁcient community to ground upon’.18 Both Mill and Bain treated Stewart’s insights as primarily of interest for lexicographers keen on disambiguating words and tracing the development of their different (polysemic) uses. Stewart, however, had been more judicious and less censorious. He had noted that where the transitive links of association are ‘slight and casual, the several meanings will remain distinct from each other, and will often, in process of time, assume the appearance of capricious varieties in the use of the same arbitrary sign’. This is the polysemic case that occupied Mill and Bain. One might characterize it as ‘a family of meanings’ (although not in Wittgenstein’s sense (see Exg. §77)). But Stewart further noted that ‘where the association is so natural and habitual as to become virtually indissoluble, the transitive meanings will coalesce in one complex conception; and every new transition will become a more comprehensive generalization of the term in question’. Here he anticipated Wittgenstein’s reﬂections on family-resemblance concepts.19

2. Family resemblance: precursors and anticipations Wittgenstein introduces the idea of family resemblance in Investigations §§65–71. The occasion is a back-reference to the essentialism of the Tractatus. One might object to the whole drift of the Investigations thus far, Wittgenstein writes, by observing that he has nowhere characterized the essence of a language-game, or of language. He has not speciﬁed ‘what is common to all these activities, and what makes them into language or parts of language’ (§65). So he is in effect letting himself off the very problems to which the Tractatus had been dedicated: namely, the investigation of the general form of the proposition and of language. He had argued there that the general form of propositions is: Things are thus-and-so — or, more explicitly, that every proposition with a sense is 18

Alexander Bain, Logic (Longmans, Green, Reader and Dyer, London, 1870), vol. 2, p. 172. His example was ‘stone’, extended from some mineral, rocky materials, but not slate, to accumulations in the gall-bladder and to the hard kernels of fruits, to some metallic ores (‘loadstone’) but not others, etc. 19 Stewart was not unique in recognizing the dogmatism of the essentialist tradition. Later in the century, William Whewell, in The Philosophy of the Inductive Sciences, 2nd edn (Parker, London, 1847), argued that classiﬁcation in natural history depends on our purposes, especially on that of framing fruitful generalizations. It is fallacious to suppose that scientiﬁc purposes demand that natural classes be deﬁned by essential characteristics. Developed branches of natural history show the successful use of classes to be determined by resemblance to paradigms (‘types’), rather than by characteristic marks. Subsequently (1901/2) William James, in his Gifford Lectures, The Varieties of Religious Experience (Lecture II), argued that the multiplicity of divergent deﬁnitions of religion ‘is enough to prove that the word “religion” cannot stand for any single principle or essence’, and that we should ‘admit at the outset that we may very likely ﬁnd no one essence, but many characters which may alternately be equally important in religion’. Similar considerations, he conjectured, apply to such concepts as government.

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either a combination of simple names that depicts a possible state of affairs, or a truth-functional combination of such propositions. And a language, he had supposed, is simply the totality of propositions thus constructible. But now he is denying that the various things we denominate ‘language’ or ‘proposition’ have anything at all in common in virtue of which we call them all ‘language’ or ‘proposition’ (PI §65). To vindicate his strategy, he must show that it is not necessary that everything falling under a given concept should have common properties, that certain concepts may have a unity and integrity that does not consist in their possession of characteristic marks. For this purpose he selects as an example the concept of a game. Given the already mooted analogy between speaking a language and playing a game, this example (if it successfully demonstrates the cogency of the idea) provides indirect support for the thought that the concept of a language is a family-resemblance one. Neither the basic idea nor the terminology of ‘family resemblance’ and ‘family likeness’ (BB 27) are novel.20 The bare idea, as just noted, is in Stewart; what is original is the use that Wittgenstein makes of it. The German terminology has an interesting history.21 The thought that various languages descend from earlier (parent) languages was mooted by many linguists in the early modern era. That the afﬁnities between a variety of languages (a family of languages) can be explained in terms of a common descent from Sanskrit was a hypothesis made prominent by Sir William Jones’s lectures,22 which in turn inﬂuenced Friedrich Schlegel; thereafter the metaphor of family was commonly applied to relationships between languages. Schopenhauer, in his discussion of morphology and the morphological method, observed that morphology ‘presents us with innumerable and inﬁnitely varied forms that are nevertheless related by unmistakable family likeness (Familien Ähnlichkeit)’.23 Humboldt compared languages and their afﬁnities with human countenances, in which ‘resemblances are recognised, but no measurement or description of the parts in detail and in their interconnection can subsume the particularity in a concept’.24 Nietzsche remarked on the ‘odd family resemblance between all Indic, Greek, and German philosophizing’, which he explained by reference to the unconscious dominance of common ‘grammatical functions’ of the various languages.25 20

The OED cites the ﬁrst occurrence of the English term ‘family resemblance’ as 1858, and ‘family likeness’ as 1766. 21 For much of the historical data, and for illuminating conversations on the subject, I am indebted to Jonathan Witztum. 22 Sir William Jones, ‘On the Hindus’ (1786), repr. in The Works of Sir William Jones, vol. 1 (G. G. and J. Robinson and R. H. Evans, London, 1799), p. 26. 23 A. Schopenhauer, The World as Will and Representation (1st edn 1818) (Dover, New York, 1958), vol. 1, p. 97, see also p. 154, and vol. 2, p. 380. 24 Wilhelm von Humboldt, On Language (1836) (Cambridge University Press, Cambridge, 1999), pp. 50f. Interestingly, Wittgenstein uses the same metaphor of ‘multiplicity of faces with common features’ in his ‘Remarks on Frazer’s Golden Bough’ (GB 143). 25 F. Nietzsche, Beyond Good and Evil (1885), §20.

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It is one thing to note family resemblances between different languages and to group the various languages into families according to their genesis. It is quite a different thing, however, to extend the notion of a family resemblance to concepts (including the concept of a language), i.e. to argue that the extension of a concept may be united not by common characteristics but by overlapping similarities between the members. Wittgenstein explained his conception, confronted arguments against it, and deployed it, ﬁrst, to undermine the essentialism that informed the philosophical tradition and that had infected his own thought in the Tractatus, and second, to shed light upon key concepts in philosophy, especially formal concepts (such as language, proposition, number) that he had once compared to variables, psychological concepts, and perhaps concepts in ethics and aesthetics (in particular good and beautiful).26 Wittgenstein’s criticisms of his earlier ‘sublime’ conception of philosophy as an investigation into the essence of the world will be discussed in ‘Turning the examination around: the recantation of a metaphysician’. Here I wish merely to draw attention to his criticisms of his youthful commitments concerning analysis and deﬁnition by characteristic marks. In the ‘Diktat für Schlick’ he said that he could not characterize his [new] standpoint better than by saying it was the exact opposite of Socrates’ in the Platonic dialogues (TS 302, 14).27 For he [now] rejects the assumption that a concept-word applies to its extension in virtue of possession of common properties. This assumption is ‘an ancient and primitive conception of the use of language’ (ibid.). He observed that ‘Plato’s way of looking for the essence of things was very like talk of looking for the ingredients in a mixture, as though the qualities were ingredients of a thing’ (AWL 34), and he linked his own earlier conception with Plato’s. Wittgenstein confessed that he had thought that an ordinary object is composed of its properties — for example, that a red circle is composed of redness and circularity — that it is a complex with these component parts (PG 200). In ‘Remarks on Frazer’s Golden Bough’ he wrote: ‘As dead as death’, ‘Nothing is as dead as death; nothing is as beautiful as beauty itself ’. The picture in terms of which one conceives of reality here is such that beauty, death, etc. are the pure (concentrated) substances, while they are present in a beautiful object 26

It is not wholly clear whether he thought that ‘good’ and ‘beautiful’ constitute families of (distinct) meanings or are family-resemblance concepts — or, indeed, whether he differentiated two distinct categories thus (M 104; AWL 34f.; CV 24; PG 77; PI §77 and Exg.). Be that as it may, in view of G. H. von Wright’s The Varieties of Goodness (Routledge and Kegan Paul, London, 1963), the characterization of ‘good’ as a family-resemblance concept is not defensible (see Exg. §77). But it would be misleading to say that the varieties of goodness constitute a family of distinct but related meanings on the linear model of linked and partially overlapping similarities. Nevertheless, Wittgenstein’s negative case is correct: ‘good’ is not deﬁnable by characteristic marks, and does not signify a simple and indeﬁnable quality either. 27 Similarly, in MS 157a, 35v, he noted: ‘Es soll alles auf die Betrachtung der Familie hin spielen, da diese erst meine Methode rechtfertigt’ (‘Everything should lead towards consideration of the family, since only the latter justiﬁes my method’).

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as an admixture. — And do I not recognize here my own observations about ‘object’ and ‘complex’? (GB 135; cf. BB 17; in BT 434 Wittgenstein added in parentheses ‘Plato’)

In his Tractatus investigations into the nature of propositions, he had laboured under the illusion of the unity of all concepts (MS 157b, 6r). He had thought that each concept is composed of its characteristic marks, and that to each name or simple concept-word there corresponds a unique entity or ‘object’ in reality, which is common to all things falling under it (MS 142, §104). So too, he had thought that ‘If one proposition is a picture then every proposition must be a picture, since they must all be of the same nature’ (MS 157a, 56r; Z §444). In short, it had not occurred to him that the unity of a concept might be derived from the family resemblances between the things that fall under it. The reason it had not occurred to him was not thoughtlessness, but rather a misconception of the role of logic and the idea that determinacy of sense is a condition of the possibility of representation. The traditional quest for essences now seemed to him to be founded on misconceptions.28 ‘The philosopher would like to penetrate to the deeper meaning which he dimly feels to lie behind these words [viz. ‘truth’, ‘sense’, ‘reality’]. For this purpose he asks: What is the essence of truth? What is the essence of the real? We are no longer tempted to give answers to these questions. But what underlies this obscure search? What force imposes these questions on us?’ (VoW 487f.). One source is the quest for deﬁnitions, coupled with the Augustinian thought that if one cannot give a deﬁnition, then one cannot say what one knows, e.g. what time is (i.e. what the word ‘time’ means). But this is a mistake. If one can use the word ‘time’ correctly, explain how it is correctly used in its various contexts, then one can say what one knows (see Exg. §75, 2.1). A related source is that important nouns, such as ‘time’ or ‘rule’, are often used in a disorderly way. Philosophers are tempted to ﬁll in the huge gaps left by the use of such words, ‘and yet precisely these gaps are what is really characteristic of the meaning of these words’. A third source is the misguided quest for analysis: This exhibits what has been the chief temptation of all previous philosophy: that is the search for formulas which are to enunciate the innermost essence of concepts. One asks: What are space and time? What is their essence? One complains that psychology has not yet unearthed the essence of consciousness. One speciﬁes as the ultimate goals of logic the fathoming of the essence of truth. And so on. . . . Indeed, doesn’t the same mistake live on in the efforts of modern logicians to represent our concepts in a sort of chemical formula, only in a more sublimated form. Typical of this is Frege’s problem: What is a number? . . . The question . . . arises from a mistaken grammatical 28

The late twentieth-century variant of the essentialist conception, and the heir to the idea of ‘real deﬁnition’, was the thought that so-called natural-kind concepts are so deﬁned as to leave a gap within the deﬁnition to be ﬁlled by scientiﬁc discoveries about the ‘real essences’ (e.g. the explanatory atomic constitution) of natural kinds.

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background; for to this ‘What?’ we imagine a ‘This’, or we expect some ‘This’ in answer. Even the tone of this question recalls the tone of Augustine’s question ‘What is time?’ A substantive misleads us into looking for a substance. (VoW 490f.)

3. Family resemblance: a minimalist interpretation The notion of family resemblance is introduced in the Investigations and clariﬁed primarily by reference to the concept of a game. It has been hailed by some as a notion of great philosophical utility, and criticized by others as illusory. The conception is not altogether clear. As Wittgenstein abandoned his early essentialism, as he relinquished the demand for determinacy of sense, and as the idea of family-resemblance concepts dawned on him, he was prone to make exaggerated claims about the indeterminacy and multiplicity of meanings. Where everything had once seemed on analysis to be crystalline and sharply deﬁned, now everything suddenly appeared to be in ﬂux. This phase passed, and by the time he wrote the Investigations, the tendency to swing from one extreme to another had been curbed. The salient points Wittgenstein makes with respect to the concept of a game are as follows. (i) To say that games must have something in common, otherwise we would not call them all ‘games’ is false. For if we look at a range of games, we see only a network of relationships and overlapping similarities. Yet we call them ‘games’ for all that (§66). (ii) Although we could draw a sharp boundary around the extension of the concept of a game, we have not done so. We use the word ‘game’ perfectly comfortably without circumscribing it exactly (cf. §§68–9). Moreover, any suggested deﬁnition would agree only in part with the actual use of ‘game’, which is uncircumscribed. Moreover, it might well be overtaken by further extensions to the family (PLP 180). (iii) The various activities called ‘games’ are so called in virtue of a complicated network of similarities (§66). Such a concept resembles a long rope twisted together out of many shorter ﬁbres (§67). It is held together by the overlapping of many similarities, similarities ‘in the large’ and ‘in the small’ (cf. Exg. §66 for the meaning of this topological phrase). (iv) The expression ‘family resemblance’, when applied to such concepts, invokes a metaphor (§67). The network of overlapping similarities constituting the concept of a game is compared with resemblances that hold between members of a family. It is not in virtue of their all having some set of common properties that we characterize members of an extended family as being recognizably Plantagenets or Tudors. (v) The explanation of what a game is consists in giving appropriate paradigmatic examples (§71), i.e. in describing games (§69). To these we may couple a similarity-clause: ‘These and similar things are called “games” ’ (§69),

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or, perhaps, a discussion of how other sorts of games can be constructed on analogy with these, or a speciﬁcation of certain activities that would not be included among games (§75). The examples are, as it were, ‘centres of variation’ (EPB 190). The crucial point is that they are meant to be taken and used in a particular way: namely, as paradigmatic examples with a normative function (§71). This form of explanation is not a ‘second best’ method (AWL 96), but is perfectly adequate. (vi) The adducing of relevant similarities justiﬁes applications of ‘game’, since it is on account of the relationships among games, especially on account of similarities with the paradigmatic examples, that we correctly call certain activities ‘games’ (cf. §§65, 67; PG 75f.; MS 140, 32). (vii) Such a series of examples together with a similarity-rider, given in an explanation of meaning, is itself a rule for the use of the expression in question (PG 272–4; AWL 96).29 (viii) Consequently, the ability to give a deﬁnition in terms of characteristic marks is not a necessary condition of understanding such a word (§70). If games have no common properties, it is impossible so to deﬁne ‘game’, and hence nobody has the ability so to deﬁne it; but it does not follow either that nobody knows or that nobody can explain what it means (cf. §§69, 75). And if games do have common properties, it need not be in virtue of these that we call certain activities ‘games’ (M 17; AWL 32; PG 75). (ix) Although everything resembles everything else in one way or another, we are able to learn the use of family-resemblance concepts from such explanations coupled with examples of application. Explanations by example sufﬁce, in such cases as ‘game’, for us all quite naturally to be able ‘to go on in the same way’.30 There is a broad consensus on application and on exclusion alike (war is highly competitive, thoroughly engrossing, there are winners and losers, and there are various rules of war — but no one would literally call it ‘a game’), and we are able to use family-resemblance concepts without radical disagreements or misunderstandings. (x) Games form a single family (§67). What holds them together and gives them a unity is the overlapping of the many similarities among games, similarities that we count, and are in agreement in counting, as signiﬁcant. In view of this unity, it is appropriate to speak of the concept of a game (the concept of number, etc.) (§§68, 70). (xi) Family-resemblance concepts are susceptible to extension by the accretion of new members to the family. The expansion of the family does not imply a change in the meaning of the family-resemblance term. So, the 29

This is akin to the fact that the rule for an arithmetical series can be given in the form of the ﬁrst few members (e.g. ‘1, 4, 9, 16, 25’) followed by an ‘and so on’. 30 This cannot, however, be generalized to all cases of family-resemblance concepts. The concept of number is said to be a family-resemblance concept, but there was nothing ‘natural’ about extending it from natural numbers to negative numbers (many mathematicians felt acutely uneasy), and nothing ‘natural’ about including quaternions.

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concept of art has (arguably) expanded to include such new relatives as ﬁlm, photography and ballet, without any change to the meaning of ‘art’, and the concept of number has been extended over the centuries to include new members in the family, such as imaginary numbers or quaternions. (xii) For special purposes we can draw boundaries around the concept of a game (§§68f.). But whether we should draw them here or there depends only on what facilitates achieving these purposes. The main thrust of Wittgenstein’s discussion is negative. His aim is to dethrone a prevalent picture shaping philosophical reﬂection on the meaning of conceptwords. But one might think that he is proposing new dogmas in place of the old. First, he afﬁrms that games have no common properties, even suggesting that we can see that they have none (§§65f.). But how could we prove this, let alone see it? Wittgenstein here advances an unnecessarily strong statement. To disprove the assertion that there must be common properties to warrant the application of a univocal expression, it is sufﬁcient to establish that there need not be any, and that is a weaker claim than that there are none. This is indeed what most parallel passages argue (e.g. M 104; BB 86f.; AWL 32; PG 75f.; PLP 180ff.). Nevertheless, the matter remains contentious. Games are played, and playing a game is a human activity — so games surely have this as a common property. Furthermore, it is difﬁcult to deny that games are rule-governed. Wittgenstein seems to agree in LWL 48, although he later mentions primitive games without rules (LWL 101). But he describes none. He mentions a child’s throwing a ball against a wall as an example of a game without winning or losing (PI §66), and this might seem to be also a case of a ruleless game. But the example is questionable,31 since the child is playing about, not playing a game. (However, the German ‘spielen’/‘Spiel’ differs from the English equivalent, the noun being an internal accusative of the verb.) Wittgenstein confronted this worry explicitly, claiming that ‘there are all sorts of intermediaries between playing games according to rules and just playing about’ (AWL 81), but, again, described none. The essential points in defence of Wittgenstein’s position are (a) that the standard speaker of our language is not aware of any properties common to all games that make them all games; (b) hence, that there is no common property or properties in virtue of which we hold all and only games to be games; (c) that we do not explain ‘game’ by enumerating characteristic marks of games; (d ) that if asked or challenged, we would justify calling some activity ‘a game’ by reference to similarities to paradigmatic examples of games, rather than by citing properties common to all games; and (e) that even if we were to discover such properties, this would not reveal the marks of our concept of a

31

Hide-and-seek would have been a better example of a game without winners and losers.

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game because they would not belong to our (present) practice of explaining ‘game’.32 Secondly, Wittgenstein implies that the similarities among games justify calling them ‘games’, and that the absence of relevant similarities justiﬁes refusing to call an activity ‘a game’. But must there always be grounds for applying or withholding the term ‘game’ — for example, for including darts and excluding archery contests? May there not just be groundless consensus? Even if there are grounds, must these always be similarities? These questions may be debated. But Wittgenstein might simply retreat to the negative observation that games (languages, numbers, etc.) have no one thing (or set of things) in common in virtue of which we use the same word for all (§65). Thirdly, the alleged unity of a family-resemblance concept seems precarious. What are the criteria of identity for a ‘family’? Why should we agree that games form one family, not several? Why does the multiplicity of possible explanations of a family-resemblance expression not show that it is polysemic, that it has a family of related meanings? Presumably Wittgenstein would argue that in polysemic cases we feel no qualms in disambiguating the old expression (e.g. ‘stone’, ‘canon’), either by supplementation (e.g. ‘gall-’,‘fruit-’, ‘key-’) or by introducing alternative terminology. But although we may distinguish different kinds of game (e.g. board games, card games, word games), and that in many different ways, we do want to subsume them all under the common concept (cf. PI §532). We do not conceive of the use of the word ‘game’ as exemplifying focal meaning as discussed by Aristotle (exempliﬁed, for example, by ‘healthy’), for (among other reasons) there is no single centre of variation. The various explanations of the word ‘game’ are interchangeable, applicable (although perhaps not always pedagogically aptly) to all cases. We do not conceive of the applicability of the common term ‘game’ to members of the family as exemplifying polysemy — they are all games in the same sense of the word (unlike gladiatorial and Olympic games). 32

It has been suggested that games are rule-governed activities, with an arbitrary and nonserious objective lacking signiﬁcance outside the game, which players set themselves to attain for the sake of the fun or the satisfaction of participating in the activity and/or attaining the objective (B. Rundle, Wittgenstein and Contemporary Philosophy of Language (Blackwell, Oxford, 1990), ch. 3, which contains an illuminating critical discussion of these matters). The ingenuity is admirable, but does not allay all qualms. Do professional players of tennis or football all play for fun or participatory satisfaction? Are war-games at the Pentagon played for fun? Are their objectives arbitrary? Do the games we get children to play to teach them to read or to do elementary arithmetic have arbitrary or non-serious objectives? However, even if we disregard these qualms, we must surely note that no one has ever acquired the concept of a game from this explanation, that we acquire the concept of a game, and can explain by examples what we mean by ‘game’, long before we can understand such a deﬁnition, and that it fulﬁls no role in our practices of teaching the use of the word ‘game’ or of applying it and adjudicating its application. If someone wants to object to Goffman’s use of the phrase ‘Games People Play’ (in his book of that title) to refer to forms of marital conﬂict, it will be because of dissimilarities to standard examples of games, dissimilarities ‘in the large and in the small’, and not because the activities in question do not fall under this sophisticated deﬁnition.

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Finally, Wittgenstein asserts that family-resemblance concepts have no sharp boundaries. Does this mean that there must be borderline cases or disputes about their applicability? Not so. Wittgenstein does not argue that family-resemblance concepts are necessarily vague or essentially contested (the concept of number is neither, for even though the general concept is not bounded, the members are clearly deﬁned, and there are no borderline cases). Their lack of sharp boundaries is just a reﬂection of their not being deﬁned by characteristic marks and their being extendable. Terms that are so deﬁned are not proof against disputed applications (How old does one have to be to be an eligible bachelor? How reﬁned must our measurements be to determine something as triangular in shape?), and family-resemblance terms are not intrinsically susceptible to them. Even when thus given the most minimal interpretation, the remarks on family resemblance are a challenge to the orthodox idea of deﬁnition as analysis. They contribute to undermining the traditional Platonist conception of deﬁnition in philosophy as a sublime quest for insight into the nature and essence of things. They question the associated conceptions of what it is to explain concept-words, to justify or criticize their applications, and to understand them.

4. Sapping the defences of orthodoxy Various strategies in defence of orthodoxy can be deployed. Wittgenstein confronts these in §§65–88. The ﬁrst strategy accepts Wittgenstein’s insistence upon a parallelism between what a word means, how we explain it, and what we understand by it, but challenges the cogency of Wittgenstein’s criticisms. This may take a number of forms. (i) Games (numbers, propositions, etc.) do share common properties, but these are disjunctive (§67(c)). (ii) Such a concept is legitimate because it is a logical sum of sub-concepts each of which is deﬁnable by characteristic marks (§68). (This involves a liberalization of the claim that whatever falls under a concept-word must share common properties.) (iii) ‘Game’ is ambiguous; there is no single concept of a game, but rather a number of closely related concepts each of which is determined by analytic deﬁnition (this might be one reaction to §§67(a), 69, 77). (iv) The concept of a game is itself a simple concept. Games have in common the property of being games, just as blue things share the common property of being blue. What §66 shows, a critic might argue, is that they have nothing else in common, i.e. that the property of being a game is unanalysable. (v) There is no such thing as the concept of a game, i.e. no such thing as a concept without sharp boundaries (§71). The word ‘game’ is useless or has no agreed use.

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(vi) The concept of a game is a ‘cluster concept’. The full explanation of ‘game’ by reference to paradigmatic examples must specify not only a set of appropriate examples, but also a set of respects of resemblance, perhaps differentially weighted, which are relevant for determining whether an activity is a game. Accordingly, the predicate ‘is a game’ may be deﬁned by stipulating that it is true of X provided that the sum of the weights of the respects in which it resembles some one (or perhaps any) of the paradigmatic examples exceeds a particular threshold value. Wittgenstein’s moves against these positions are obvious in the text (see Exg.), except for (iv) and (vi). Clearly he would argue that (iv), like (i), distorts the concept of a common property. The objection to (vi) would be simply that such a calculus of thresholds and weights is not part of our explanation of ‘game’, and hence not a part of what we understand given the assumption that what is explained by an explanation of meaning is what is understood when the meaning of an expression is understood. The second line of defence is constructed on the repudiation of this assumption: our understanding of a concept-word may go beyond our explanations of it, and therefore inability to deﬁne it does not prove that the objects falling under it do not share common properties. This too may take different forms. (i) An explanation of ‘game’ by examples is an indirect means for conveying to another knowledge of the common properties that make activities into games. These properties are not expressed or put into words, but someone who understands ‘game’ as a result of the explanation must see what the examples have in common (§§71f.). (ii) An explanation by examples is successful only if the learner acquires from it a general idea (a mental image), as the empiricists argued, of what is common to all the examples; only if he has such a general idea can he apply the word to fresh instances (§73; cf. BB 27f.). (iii) A particular experience in conjunction with the examples, e.g. seeing them in a certain way, is essential to achieving understanding from an explanation by examples (cf. Exg. §74). These arguments treat explanations by examples as the basis for understanding, but each, in a different way, takes the explanations to stand in need of supplementation to constitute a correct account of what we understand by the explananda. Wittgenstein’s objections are explicit in §§71–4 (see Exg.). The outermost line of defence drops the assumption that there is any relation between explanations and what we understand by the concept-word in question. An explanation of ‘game’ by examples has nothing to do with knowing what a game really is. Understanding the word ‘game’ consists in using it according to certain deﬁnite rules hidden in the medium of the mind, and there is no reason to suppose that these must be related in any way to what we say when asked to explain what ‘game’ means. Indeed, divergence is held to be shown by the fact that what we mean and understand by ‘game’ is something deﬁnite, whereas what we say in explaining ‘game’ gives the concept

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no sharp boundaries. The system of hidden meaning-rules operated unbeknownst to us by our minds must be perfectly general speciﬁcations of the circumstances in which words are to be used. Within this limitation, the rules may have a variety of forms: the speciﬁcation of characteristic marks, the construction of the concept out of sub-concepts by means of truth-functions, or the calculus of weighted degrees of resemblance and thresholds of ‘cluster concepts’. The crucial point is that mental operations are essential to meaning, and they conform to the orthodox conception of the meaning of concept-words. Explanations do not so conform, but that merely shows the gap separating them from what is understood. Wittgenstein’s immediate moves against this position (which characterized the Tractatus (TLP 4.002)) are developed in §§75–87. They can, however, be seen aright only once the the concepts of meaning, understanding and thinking have been fully clariﬁed (§81). Meaning something is not an act or activity, understanding is not a state, and thinking or reasoning is not a process. These concepts, misconstrual of which lead us astray over a wide ﬁeld, will be investigated in the sequel. There are still three lines of retreat open to the defenders of orthodoxy. The ﬁrst would be to drop the assumption that the existence or non-existence of common properties among things falling under a concept-word is in any way related to what it is to understand such a word. One might concede that understanding ‘game’, knowing how to use the word, does not presuppose knowing what games have in common, any more than, according to Frege, understanding, i.e. mastery of the use of, number-words presupposes knowing what numbers have in common (‘Often it is only after immense intellectual effort, which may have continued over centuries, that humanity at last succeeds in achieving knowledge of a concept in its pure form’). Nevertheless, games must have something in common. The second would be to object that a concept-word that is neither the name of a simple indeﬁnable quality nor susceptible to an analytic deﬁnition is not ﬁt for use in science or other serious inquiries into truth (as Mill and Bain argued). The third would be to insist that an apparent concept-word that does not satisfy Frege’s demands for completeness of deﬁnition (determinacy of sense) is not a genuine concept-word at all. In Wittgenstein’s view, the ﬁrst line of retreat is futile. Whether the objects falling under a concept share common properties is only of any philosophical interest on the assumption that this question bears on our understanding of concept-words. The second line of retreat Wittgenstein cuts off in a coda (§88, see Exg.). He criticizes its notion of what is perfect or ideal as rooted in misunderstanding. The third he dismisses for two reasons (§§80, 84–8 and Exg.). On the one hand, no explanation has to determine for every possible object under every possible circumstance whether it falls under the concept or not. An explanation need only distinguish the explanandum from things with which it might be confused. So it is not necessary to distinguish by means of a deﬁnition between

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propositions and chairs (BT 60), which (logically) could not possibly be confused. On the other hand, the idea that an adequate explanation must determine the application of an expression in all possible circumstances is incoherent (is there such a totality?). It needs to establish a pattern of use only in circumstances that actually arise. It could not, pace Frege (BLA ii §56), settle every possible doubt (is there any such totality?). It needs to resolve only doubts that might actually arise but for the explanation.

5. Problems about family-resemblance concepts There are many further questions about family-resemblance concepts. Philosophers have been quick to raise them, and many have found Wittgenstein’s answers inadequate. But since he introduced the notion largely for a negative purpose, there was arguably no need for him to give a more general account. These questions arise primarily when the idea is used for purposes different from his. (i) Bounds. How are the lines of demarcation to be drawn between familyresemblance concepts and other kinds? What feature makes a concept into a family-resemblance concept? Wittgenstein leaves much unclariﬁed. Family-resemblance concepts are associated with a characteristic form of explanation of meaning: the speciﬁcation of a set of paradigmatic examples (with an explicit or implicit similarity-rider). But the boundaries of this form of explanation are unclear. Wittgenstein’s explanations of ‘game’ and ‘number’ specify types of things as paradigmatic examples; e.g. type-activities, like ‘chess’ and ‘football’, or types of numbers, like rationals or reals. But we might explain ‘game’ by pointing to a number of token-activities (particular games of chess, football, patience, etc.), perhaps adding that things like these are called ‘games’; or we might explain ‘number’ by citing paradigms such as 2, −1, √2, 2 + i, and √2 + 3i − j − 2k. Would these count as explanations of the same form? These qualms rest on unwarranted preoccupation with form and inadequate attention to the use of examples as explanations of meaning and as constituting rules for the application of words in our practices (AWL 96). It may well be that we should treat explanations by paradigmatic examples as themselves constituting a family. But in the absence of some special purpose, there is no point in drawing a sharp boundary around them, and Wittgenstein certainly does not do so. There is further uncertainty about the bounds of family-resemblance concepts. How is the categorization of concepts related to the classiﬁcation of explanations? One possibility would be that we characterize as a family-resemblance concept any expression whose explanation may take the form of an explanation by a range of examples. This would be misguided. That we can explain what a natural number is by a series of examples does not preclude giving a

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sharp deﬁnition. And that we can explain what red means by giving a series of examples of red things does not make red a family-resemblance concept.33 The antithetical possibility would be to characterize as a family-resemblance concept any expression whose complete explanation in our practices does take the form of an explanation by examples and does not include analytic deﬁnitions. (ii) Coherence. Is any family-resemblance concept coherent? If it is explained only by reference to some paradigmatic examples together with a similarityrider, then it must be essentially unbounded (cf. PG 76). According to this explanation, one might think, everything will be subsumable under the concept. For everything resembles everything else in some respects, and given any two things, we can construct a chain of intermediate cases in which each neighbouring pair is linked by many similarities. Hence, since nothing could fail to fall under any concept so explained, any family-resemblance concept is vacuous. This is misconceived. One needs to look at our practice of using the expression. The important facts are (a) that there is a general consensus over the application of ‘game’, for example; (b) that we do not explain it by characteristic marks; (c) that we do not apply it to anything whatever, and that we do not accept any arbitrary resemblances as warranting the extension of the term; (d ) that we accept (as correct) explanations that enumerate examples; (e) that we justify calling a novel activity ‘a game’ by reference to its similarities to some existing paradigm or paradigms. It is not, and cannot be, the proper business of philosophy to construct an explanation for how what is actually the case is logically possible. Rather, one must show what is wrong with the thought that it is logically impossible. That is, again, a matter of directing attention away from the form of explanations by examples to the use that is made of them. ‘A rule that can be applied in practice is always in order’ (PG 282), i.e. is not logically defective. (iii) Applications. Is it possible to justify or criticize applications of familyresemblance concepts? And, if so, are the only relevant grounds similarities and dissimilarities? Wittgenstein suggests a positive answer to both questions in saying that it is in virtue of the relationships between the phenomena called ‘language’ that we call them ‘language’ (§65). That we can justify or criticize applications of family-resemblance concepts seems a natural generalization from Wittgenstein’s examples. There is surely something to discuss about whether shooting is a sport or gladiatorial combat a game. ‘Why do you call it “a game” (or “a sport”)?’ seems a legitimate question, and the retorts ‘Just look at it!’ 33

It is important not to confuse paradigms used as samples in an ostensive deﬁnition with paradigmatic examples used in an explanation of a family-resemblance concept. Something is red if it is the colour of the sample (not: if it resembles the colour of the sample; red is a monadic, not a relational, predicate). An activity is a game if it resembles, in appropriate ways, a paradigmatic example or limited range of examples of activities we deem games. The deﬁning sample belongs to the method of representation; the explanatory examples do not.

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or ‘Can’t you see?’ are unacceptable in hard cases. On the other hand, must justiﬁcation and criticism be limited to appeals to degrees of resemblance and dissimilarity with standard examples? Must that alone be relevant in an argument about whether blood sports are really games? One might think that distinguishing between games and rituals, between games and theatrical performances, or between games and forms of warfare is not just a matter of totting up the numbers and degrees of resemblances between such activities and paradigmatic games. Reaching a verdict on this issue depends on Wittgenstein’s notion of ‘similarities in the large’ (cf. Exg. §66), which is not properly explained. The sorts of consideration that would be adduced in denying that eighteenthcentury battles were games (e.g. their socio-political consequences, the loss of life attendant on them) might well be subsumed under ‘dissimilarities in the large’ (the difference between similarities in the small and in the large is whether they are noted by looking at or around the phenomena). These, it might be argued, sufﬁce to defeat the support given by the multitude of patent similarities between games and eighteenth-century battles. One may grant that battles resemble games in certain respects, but they resemble quarrels in more important respects. There is nothing arbitrary in our refusal to count battles as games people play. On the other hand, it is less than obvious whether it is because of lack of similarities that Oxford Torpids or Eights, say, does not count as a game, whereas tag or hide-and-seek does. How the general issue is to be settled is perhaps irrelevant if the concept of family resemblance is used only for Wittgenstein’s purposes. (iv) Range. What is the range of family-resemblance concepts? What concepts fall within this class? Are there any kinds of concept all of which or none of which fall within it? An expression introduces a family-resemblance concept only if it is not part of our practice to deﬁne it by characteristic marks. So too, expressions deﬁned by reference to samples (as opposed to examples) are excluded. Deﬁnability by analytic deﬁnition is a feature of a concept-word within a given form of representation and relative to its norms of explanation. That we might, with sufﬁcient ingenuity, concoct a deﬁnition does not show that, contrary to our previous beliefs, it really has an analysis in our practice of using the expression. Analysis is neither discovered nor concealed, but stipulated or constructed. Nevertheless, it may be important to note that certain kinds of concept are unanalysable relative to certain systems of other concepts, and it may be helpful to characterize some such classes as consisting of family-resemblance concepts. The importance of this turns on the inclination to misconstrue concepts of certain kinds. For, in certain cases, we readily construct a mythology to explain away the appearance of unanalysability. Wittgenstein concentrates on two such cases: formal concepts (e.g. proposition, proof, language, name, number) and psychological concepts (e.g. thinking, understanding, intending, believing, trying). Most of the concepts that he asserts to be family-resemblance concepts fall into one or the other of these classes. In the ﬁrst case, the temptation is to suppose that all the things falling under a

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formal concept share an essence, but that we cannot say what this is (cf. TLP). In the second case, the temptation is to compensate for the absence of patent mental phenomena common to all the things falling under a psychological concept by postulating latent ones ‘buried deep in the unconscious mind’, or to postulate mental processes that are too swift to apprehend (TS 302, 13ff.; PG 74f.; MS 152, 5 (see Exg. §165)). Wittgenstein invokes the notion of family resemblance primarily as an antidote to these temptations.

6. Psychological concepts In the early 1930s the notion of family resemblance was prominent in Wittgenstein’s discussions of psychological concepts. It crops up in his account of such verbs as ‘think’, ‘expect’, ‘know’, ‘intend’, ‘wish’, ‘mean’, ‘understand’, ‘read’, ‘calculate’, ‘derive’, ‘believe’, ‘observe’, ‘compare’, ‘being guided’, ‘try’,‘motive’ (TS 302, 13f., 25f.; PG 74f., 141; BB 17ff., 32f., 86, 113–20, 124f., 144f., 152; PLP 183ff., 351f.). Wittgenstein emphasized that each of these expressions is applied to a family of cases. His purpose is mainly negative: to release us from a ‘primitive conception’ of language that obscures our view of psychological concepts. The dominant consideration in these early reﬂections is that such psychological concepts do not signify a common characteristic in virtue of which we ascribe them to ourselves and others. Understanding, Wittgenstein emphasizes, ‘is not the name of a single process accompanying reading or hearing, but of more or less interrelated processes against a background, or in a context, of facts of a particular kind’ (PG 74). We are prone to think that understanding (and so too thinking, knowing, wishing, intending, etc.) signiﬁes a single process, and when we fail to identify one that is present in all cases, we jump to the conclusion that it is a mysterious process that awaits discovery.34 In fact, he suggested, ‘understand’ signiﬁes a whole family of related processes. Similarly, he argued, ‘expecting’ does not signify a particular mental state common to all cases of expectation. Suppose I am expecting someone for tea: At four o’clock I look at my diary and see the name ‘B’ against today’s date; I prepare tea for two; I think for a moment ‘does B smoke?’ and put out cigarettes; towards 4.30 I begin to feel impatient; I imagine B as he will look when he comes into my room. All this is called ‘expecting B from 4.00 to 4.30’. And there are endless variations to this process which we all describe by the same expression. If one asks what

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As Frege observed, ‘grasping (Erfassen) . . . is a mental process! Yes, indeed, but it is a process which takes place on the very conﬁnes of the mental . . . in grasping . . . something comes into view whose nature is no longer mental in the proper sense, namely the thought; and this process is perhaps the most mysterious of all. But just because it is mental in character we do not need to concern ourselves with it in logic’ (PW 145).

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the different processes of expecting someone to tea have in common, the answer is that there is no single feature in common to all of them, though there are many common features overlapping. These cases of expectation form a family; they have family likenesses which are not clearly deﬁned. (BB 20)

This is unsatisfactory, as Wittgenstein came to realize. The supposition that understanding what is said is sometimes just this accompanying process, sometimes that one, or that expecting someone to tea is sometimes looking in one’s diary and sometimes making tea, is surely wrong. We must distinguish, as Wittgenstein later did, between the phenomenological accompaniments that may accompany understanding something said or read and the understanding, as we must distinguish the behavioural criteria for ascribing a psychological predicate to another person in a certain circumstance from the psychological attribute thus ascribable. Expecting is neither a family of sensations, thoughts and mental images or a family of different kinds of behaviour, nor a family of inner and outer processes. Similarly, understanding is not a family of experiences that may occur when one understands what is said, nor is it a family of actions one might do when one understands what is said. Wittgenstein came to realize that a wide range of psychological verbs in the ﬁrst-person present tense are not used primarily to describe an inner state or process one is in or undergoing even if they can be so used. ‘I am in pain’ has a typical use as an expression of pain, rather than as a description of how things are with one. ‘I am expecting N.N. for tea’ is no more a description of my state of mind than is ‘I expect you to be there!’, even though ‘I have been expecting him all afternoon, I keep on looking at my watch, and trying to imagine what he looks like after all these years, and whenever the bell goes my heart jumps’ is a description of my state of mind. Many psychological verbs, such as ‘understand’, ‘know’, ‘believe’, ‘intend’, ‘mean’ are virtually never used to describe one’s mental state or mental processes. But they are not used to describe families of behaviour and action either; rather, the criteria for their application in the third-person case are appropriate behaviour and action in given circumstances. This does not preclude arguing (rightly or wrongly) that ‘understand’ or ‘think’, for example, is a family-resemblance concept. One may plausibly claim that understanding utterances, music, painting, women, politics, life, etc. have no common properties in virtue of which they are all cases of understanding, but rather are linked by overlapping similarities. Similarly, the reﬂective thinking of Le Penseur, the thoughtful game of the tennis-player, the thinking of the surgeon conducting an operation, the idle daydreams of the sunbather, the thinking of the skilful debater in the cut and thrust of disputation, qualifying an assertion (‘I think he is in London’), opining (‘I think this is the best’), assuming (‘I thought the bridge was safe’), presupposing (‘I thought that there was a French monarch’), etc., are not all cases of thinking because of possession of common properties. But realization of the logical character of psychological concepts does preclude the kind of argument Wittgenstein originally offered in

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the above quotation. It is noteworthy that in his subsequent writings on the philosophy of psychology, this kind of argument disappears.

7. Formal concepts In the Investigations the primary application of the notion of family resemblance is to what Wittgenstein had once held to be formal concepts (and to be akin to the variables in a perspicuous concept-script). In the Tractatus (4.126) they were thought to have as their formal characteristic marks the common properties of all their values. The Investigations holds that ‘proposition’, ‘language’ and ‘number’ (§§65, 67f., 108, 135; perhaps also ‘name’ in §38) are familyresemblance concepts that have no characteristic marks, but are explained by reference to paradigmatic examples. It is remarkable that in earlier texts, the notion of family resemblance is not applied to formal concepts, even though the idea of such an application seems very close to Wittgenstein’s thought. He emphasizes that such expressions as ‘proposition’, ‘number’, ‘rule’ and ‘word’ are explained by examples; that such concepts go as far as similarities with such examples; and that they have blurred boundaries (BT 60, 70; PG 112ff.). He also suggests that we do not call things ‘rules’ because there is something common to them all, but rather because there are many analogies between them (cf. BT 68; PG 117), yet refrains from invoking family resemblance here. Its explicit application marks a further development. The things called ‘proposition’ or ‘language’ are families of structures related to each other in complicated ways; they have neither the formal unity nor the formal equivalence that Wittgenstein had once imagined (PI §§96, 108). Such words must be brought back from their philosophical to their everyday use (PI §116). It seems evident that part of the stimulus for the change in Wittgenstein’s viewpoint was the collapse of the crystalline Tractatus conception of the proposition, and hence of language. That conception had led him to exclude from the domain of propositions a wide range of things that we do conceive to be propositions, viz. propositions of arithmetic and geometry, of ethics and aesthetics, and of religion; also the propositions of the Tractatus itself — many of which he would later subsume under the category of ‘grammatical proposition’. But with the collapse of the concept of the logically independent elementary proposition and the abandonment of the thesis of extensionality, and subsequent collapse of the crude distinction between ‘genuine propositions’ of immediate experience, hypotheses and mathematical propositions, the rationale for the dogmatism evaporated. Many different kinds of linguistic structures are propositions, and their relationships to grounds, veriﬁcation, truth and falsehood, sense and nonsense, doubt and certainty, knowledge and belief, are very varied indeed. A language is not deﬁnable as the totality of propositions that can be generated from some basic stock by a limited range

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of operations. A language is a motley of language-games. These may be very different from each other, and none is essential to what we call ‘language’. Indeed a language need contain no propositions at all, since a language containing only imperatives is perfectly conceivable (PI §18; TS 302, 27). It is on the basis of such considerations, it seems, that Wittgenstein moved from his early to his later conception. These are weighty. But whether they warrant the claim that the concept of a proposition, for example, is a familyresemblance one may still be unclear. For, to be sure, one mark of a proposition, as Wittgenstein notes, is being either true or false (PI §136). And that is a perfectly familiar property of propositions. So it is not true that there is nothing in virtue of which we call something a proposition. To this his reply was that we cannot use the characteristic of being either true or false to determine whether something is or is not a proposition as we can use the characteristics of being a man and being unmarried to determine whether a person is a bachelor. It is perfectly correct that we call ‘a proposition’ only what can be true or false. But in this context to say, ‘Every proposition must be true or false’ is as worthless (and misleading) as saying that every chess piece must obey the rules of chess. For it is not as if we have a concept of a chess piece, and then make sure that it obeys the rules; rather, what is called ‘a chess piece’ is a piece that is used in the game according to the rules (VoW 381 (F 55)). Similarly, truth and falsehood cannot be used to determine whether something is a proposition or not. Rather, to say that a proposition is whatever can be true or false ‘can say no more than that we only predicate “true” and “false” of what we call a proposition’ (PI §136). Moreover, he might have argued, what it is for an avowal, a third-person psychological proposition, an empirical description, a common-or-garden empirical hypothesis, a scientiﬁc hypotheses, a proposition of logic, a mathematical proposition, a grammatical proposition, a proposition of ethics, aesthetics or religion, etc. to be true varies from case to case (without any ambiguity in ‘true’). We explain what it is for a proposition of a given type to be true by reference to the kind of proposition it is, not vice versa (see ‘Truth and the general propositional form’, sect. 5). We do not explain such words as ‘word’, ‘proposition’, ‘name’, ‘object’, ‘number’, ‘language’ or ‘rule’ by giving analytic deﬁnitions, but rather by giving examples. This absence of deﬁnitions is not to be explained by claiming that the characteristics of formal concepts are ineffable. Expressions such as ‘word’, ‘proposition’, ‘number’ are part of everyday language and have a determinate use. These concepts are what we must clarify, not some other a ethereal concepts that we do not in fact deploy (PI §108; PLP 82ff.). Of course, we can reﬁne them for specialized purposes, but in their common-or-garden use, they are only as reﬁned as we need them to be for unspecialized purposes. Resemblance with paradigmatic examples is a matter of degree; in some cases it leaves us free to decide whether or not to extend a concept thus explained to new types of case. We are at liberty to widen or narrow such concepts as that of proposition (PLP ch. XIV; PG 117), ostensive deﬁnition (PLP 106ff.),

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number,35 rule of grammar (PLP 58ff.), etc. Our freedom is not, as it were, one of movement within a given logical space, but rather the freedom to extend or alter this space itself (BT 61; cf. PG 115). And whether to do so in a particular case can be debated, as indeed it was on the introduction of negative numbers from Indian into European mathematics. Wittgenstein’s conception of family-resemblance concepts is controversial. Although not all is clear about it, his applications of it are revolutionary and, within this range, tolerably perspicuous. It serves the negative task of shaking us free from the illusions of real deﬁnitions, of the mythology of analysis as disclosing the essences of things. It raises important questions concerning the relationship between meaning, understanding and explanations of meaning, which, at the very least, cast doubt on the idea of disclosing the meanings of terms by novel analytic deﬁnitions. And it powerfully challenges the dogma of supposing all univocal concept-words to be applicable in virtue of common characteristics shared by all the things that fall under them.

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Cf. F. Waismann, Introduction to Mathematical Thinking, tr. T. J. Benac (Hafuer, London, 1951), pp. 235ff.

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

XII

Proper names 1. Stage-setting The subject of proper names has preoccupied modern philosophers of logic and language for well over a century. It was not at the centre of Wittgenstein’s concerns. When he wrote the Tractatus, the concept of a simple name (or ‘logically proper name’ in Russell’s terminology) was indeed pivotal to his enterprise (see ‘Logically proper names’). But the idea of a simple name was far removed from that of ordinary proper names. Wittgenstein, in so far as he gave the matter any thought at all, apparently followed Russell in assuming that the latter can be treated as equivalent to deﬁnite descriptions. He took it for granted that the sentences of natural language would, on analysis, shed the conversationally convenient but seemingly logically misleading load of ordinary proper names. In the early 1930s, the example of proper names of people became relevant to Wittgenstein’s writings for one sole purpose. It was by reference to the use and explanation of a proper name (‘Moses’) that Wittgenstein illuminated the thought that the expressions of our language need not be either simple and indeﬁnable, on the one hand, or have a meaning that can be given by a sharp deﬁnition specifying necessary and sufﬁcient conditions for their application, on the other. Pace Frege and the Tractatus, they may have a family of meanings, or a blurred meaning, or a ﬂuctuating meaning. It is striking that the relevant dictations to Waismann that discuss the proper name ‘Moses’ are not entitled ‘Proper names’ but ‘Vagueness’ ( VoW 213). The precipitate of Wittgenstein’s various writings on this theme is to be found in §79 of the Investigations (see Exg.). This does not exhaust what he had to say about such names. But the rest is incidental. Waismann’s discussion of proper names in The Principles of Linguistic Philosophy (PLP ch. X, §1) is a little more extensive (and may well be derived from Wittgenstein (cf. PG 202f.). But it is noteworthy that there is no detailed discussion of the topic in Wittgenstein’s works. Nevertheless, Wittgenstein’s brief remarks have occasioned debate. In particular, on the strength of a misinterpretation, he has been taken to be advocating a so-called cluster theory of proper names. Clarifying why that is a mistaken interpretation, and why it stands in the way of the very point that Wittgenstein was trying to establish, is one of the objectives of this essay. Another is to shed light on Wittgenstein’s error in ascribing a meaning — albeit not a

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ﬁxed one — to proper names. The fact that we do not ask after the meaning of the proper name ‘Winston Churchill’ or ‘Jeremiah Johnson’ is not an arbitrary linguistic accident. On the contrary, it reﬂects important aspects of the practice of employing proper names. Although, as will be argued, Wittgenstein erred, his general reﬂections about meaning (meinen), understanding and explanation suggest that he should have been sympathetic to the view that personal names do not have a meaning (Bedeutung), not even a ﬂuctuating one, that is equivalent to that of an identifying description or descriptions, which determines their reference. On the other hand, it should be stressed that there is ample reason for thinking that he would not have had any sympathy with one variant of such an anti-descriptivist view: namely, the ‘causal theory’ of names. According to that conception, the reference of a proper name is determined by the name’s being causally linked to its referent — by way of an initial ‘baptism’ that ﬁxes the reference of ‘N’, together with the transmission of the use of the name from generation to generation. Such a causalist conception severs the reference of a given proper name from what a user of the name means by it, and thereby drives a wedge between a person’s using a name and his knowing of whom he is talking. Before commencing, some features of proper names should be called to mind. The kinds of individual things to which we give proper names are very various. They are, above all, human beings (occasionally toys, pets, valued artefacts, etc.) and places, geographical (landmarks, including mountains, valleys, rivers and lakes) and constructed (in the landscape and townscape alike) as well as ﬁxed objects at places. Such nominata are relatively persistent, typically readily identiﬁable and re-identiﬁable items in the lives of any member of a human community. Why should we give them proper names? — Among other things, they are, for one reason or another, of concern to us. We want or need to identify, re-identify and refer to them over time, and want or need to refer others to them. Of course, many other kinds of things are also given proper names — not only individual human beings but also families, tribes, nations, not only individual things but also types, not only places but also times (days of the week, festivals), and so forth. The uses of proper names are also very various. We use personal names not only to refer to people, but also to call, greet or introduce them (or ourselves), and address or entreat them. We use inscribed proper names of people to send messages to them; we use written names as labels of identity or residence, as place-holders at dinner parties, and as marks of ownership. Proper names have a use as signatures, autographs, in religious rituals, oaths and curses. (This diversity is obviously not paralleled in the case of proper names of the inanimate, although here too there is more to a proper name than a mere referential device, for we use proper names of countries, cities, places or buildings as letterheads, as parts of addresses, on signposts, maps and atlases, on T-shirts, key-rings, etc.) Partly due to compositionalist conceptions of sentence-meaning and computationalist conceptions of understanding, the primary philosophical interest

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in proper names over the past century has been in their referential role. However, it would be cavalier to assume that the only aspect of proper names that is of any moment is their referential role, and rash to tailor the description of the uses of proper names to such compositionalist preconceptions. We often give the same name to different individuals (people, places, etc.). But it is question-begging to conceive of such names as polysemic. Further, it is misleading to think that there are as many distinct names typographically represented by ‘John Smith’ as there are individuals named ‘John Smith’, i.e. to suppose that identity of bearer is a necessary condition for identity of name. This misrepresents the fact that names are typically drawn from a common stock, often chosen in accordance with predetermined conventions, and that many individuals have the same name. Proper names belong, together with deﬁnite descriptions and demonstratives, among the devices for singular reference. But it would be misguided to differentiate them from descriptions and demonstratives by taking them to have a context-invariant reference. They are, it is sometimes held, rigid designators, referring to the same individual with respect to every possible world. Alexander (the Great), we may exclaim, might not have been king of Macedon, but he could not have failed to be Alexander (no matter what he was called)! But this is misleading. For a name ‘N’ that referred to an individual at one stage may subsequently cease to do so, and that person may thenceforth cease to be N. So, for example, Abram became Abraham and ceased to be Abram, and after his conversion Paul was no longer Saul. Daisy Doe, after her marriage to Sir Richard Roe, ceases to be Daisy Doe and becomes Lady Roe. A source of interminable debate among philosophical logicians is the fact that many names, and indeed kinds of names, lack a bearer or lack reference (these should not be equated — we perfectly unproblematically refer to things that do not exist). Two tendencies should be resisted. The ﬁrst is the tendency to treat all kinds of so-called empty names as similar, thus masking differences between proper names in ﬁction (e.g. ‘Mr Pickwick’, ‘Xanadu’), in religion (e.g. ‘Zeus’, ‘Baal’), in myth (e.g. ‘Pegasus’, ‘Hercules’); also names of imaginary individuals (e.g. ‘Kilroy’), imaginary individuals in ﬁction (e.g. ‘Mrs Harris’ in Martin Chuzzlewit, or ‘Bunbury’ in The Importance of Being Earnest), and, indeed, proper names of non-existent objects in science (e.g. ‘Vulcan’, the supposed intra-Mercurian planet). An apparent common feature of greatly disparate language-games is taken to justify uniform treatment. But arguably the different language-games should be described individually, and then these uses of names lacking a bearer will be seen to be very different. The second tendency is to devise strategies to explain away ‘empty’ names — for example, by invoking realms of subsistence, or extending ontology to ﬁctional universes of discourse, or, alternatively, by arguing that such expressions are not really names, but abbreviated descriptions, or that in ﬁction names are not used to refer, but only to pretend to refer. These strategies share a common unease

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about the claim that ‘N’ is a proper name yet lacks a bearer that exists (or existed), a common presumption that to lack a bearer is to lack reference, and a common proneness to disregard the diversity and character of the languagegames in which such names are at home. As noted above, one reason for ascribing a meaning to proper names has been the compositionalist thought that the meaning of a sentence (conceived as the proposition, or thought, or sense expressed) is composed of the meanings of its constituents, and the correlative computationalist idea concerning understanding: namely, that we are able to understand sentences in use because we derive what is meant by the use of a sentence from our knowledge of the meanings of its constituents.1 Truth-conditional theories of meaning that ﬂourished in the second half of the twentieth century held the meaning of a sentence (or sentence-radical) to be its truth-conditions. The truth-value of a sentence was held to be a function of the references of its constituents. So the meaning of a proper name was sometimes held to be the manner in which it determines its reference, and hence too its contribution to determining the meaning, i.e. truth-conditions, of any sentence in which it occurs. Equating proper names with deﬁnite descriptions seemed to ﬁt the bill. But such ascriptions of meaning to proper names were motivated not by insights into the actual functioning of such linguistic devices, but by theory-driven prejudices about how proper names must function.

2. Frege and Russell: simple abbreviation theories On the grounds of a footnote (SM 27 (158) n. 4), it is common to attribute to Frege an abbreviation theory of ordinary proper names. He argues that the sense (Sinn) of a proper name, e.g. ‘Aristotle’, may differ from person to person — one person may take the sense of ‘Aristotle’ to be given by the description ‘the pupil of Plato and teacher of Alexander the Great’, while another will understand its sense as ‘the teacher of Alexander the Great who was born in Stagira’. However, Frege never explicitly states that proper names are disguised (abbreviated) deﬁnite descriptions, and elsewhere in his writings (PMC 80) he intimates that different ways of recognizing an object (e.g. a mountain seen from different viewpoints) as the referent of two different names (‘Aﬂa’ and ‘Ateb’) sufﬁce to attribute a different sense to each name, without committing himself to the doctrine that the sense of a name is always equivalent to a deﬁnite description. 1

There are some stresses and strains here. What is said or expressed by the use of a sentence has variously been denominated its ‘sense’ (or ‘the thought’ it expresses), its meaning (or ‘the proposition’ it expresses), or ‘what is said’ (or ‘the statement’ made). But it is mistaken to identify the meaning of a sentence with what is said by its use, although the latter can often be identiﬁed with what is meant by it. Similarly, the proposition expressed by the use of an appropriate declarative sentence is not the same as its meaning.

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Frege, and many other philosophers too, take for granted that an explanation of who N is, or at least one which provides a means of unique identiﬁcation, is an explanation of the meaning (or, in Frege’s technical terminology, the sense) of the name ‘N’. Frege held that the logical structure of a sentence was essentially complex, consisting not of subject and predicate, but of argumentexpression and function-name. The argument-expression picks out an object, which the designated function (a ﬁrst-level concept) maps on to a truth-value. The sentence is conceived to be the name of a truth-value, which it presents as the value of the function for the argument in question. The sense of the sentence (the thought (or proposition)) is what is understood in grasping what is expressed. Crucially, Frege committed himself to a compositionalist conception of the sense of a sentence: it is composed of the senses of its constitutive expressions. So proper names must have a sense that determines the object they stand for (their Bedeutung) and that is part of the sense of the sentence. Frege did not apparently notice that his assumption that names have a sense (or meaning, as we would say) that determines its referent commits him to individuating names by their bearers. He did notice, as the cited example shows, the variability of explanations of a given name (individuated by its bearer). However, his admission that different explanations betoken different senses is not trivial. For it threatens the assumption that it is shared sense that makes communication possible. Frege’s response was to treat the variability of explanations of names as a defect of ordinary language to be eliminated in an ideal language. N’s name has a multitude of distinct senses, but this is tolerable since they all determine the same referent, and our primary interest is in the truth-value of statements, not the identity of the thought expressed. This is inadequate — for part of the point of introducing the notion of sense was to explain shared understanding in terms of identity of sense. But, by Frege’s admission, ordinary names are a counter-example to this thesis; yet successful communication does occur. Moreover, since he holds that ﬁctional names, e.g. ‘Odysseus’ (SM 32 (162)), have sense but no referent (no Bedeutung, as he misleadingly puts it), he cannot brush aside differences of sense as no impediment to understanding on the grounds of identity of referent. Whether Frege was or was not an ‘abbreviation theorist’ is debatable. But Russell’s position is unequivocal: ‘The names that we commonly use, like “Socrates”, are really abbreviations for descriptions’ (PLAt 178). Accordingly, he denied that ordinary proper names are really names at all (from ‘a logical point of view’). The following ﬁve points support an abbreviation (disguised description) account of proper names. (i) Uniquely identifying descriptions provide a means of identifying the referent of a name, which is one role for which the notion of the meaning of proper names was introduced. (ii) Descriptions, if substitutable for names, provide one possible strategy for avoiding paradoxes arising out of sentences of the form ‘x exists’ / ‘x does not exist’.

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(iii) The cognitive non-triviality of non-trivial identity-statements (e.g. ‘Hesperus is Phosphorus’) is rendered perspicuous on the assumption that the two co-referential names have distinct meanings given by different descriptions. (iv) It explains how a sentence containing a name without a bearer nevertheless means something, given the compositionalist preconception that what the sentence means is composed of the meanings of its constituents. (v) It explains how a name, which is the name of more than one individual, can be used to refer to only one of them on a given occasion. Against this simple abbreviation account the following arguments can be mustered. First, contrast proper names with deﬁnite descriptions. (a) The question ‘Who was the victor of Austerlitz?’ typically requires the answer ‘Napoleon’, not ‘The husband of Josephine’. (b) The victor of Austerlitz was named, christened, called ‘Napoleon’ (or ‘Napoleone’), but is correctly described as the victor of Austerlitz. He became, and then ceased to be, the Emperor of France, but did not change his name; nor, arguably, did his name change its meaning. (c) People are given, have and sometimes change their names; descriptions apply or fail to apply to them. A husband gives his wife his name, but that is not the same as giving her his description. (d) The question ‘What does “the man who broke the bank at Monte Carlo” mean?’ is a request for an explanation of the meaning of the description, and is incorrectly answered by ‘N’. The latter answer would be appropriate only for the question ‘Who broke the bank at Monte Carlo?’ Second, who N is, is often not explained by description but by ostension, introduction or self-introduction. Although a description can be milked out of the ostensive explanation or introduction, it is not obvious that the name has not been understood until a deﬁnite description has been squeezed out. Third, if N’s name ‘N’ (disregarding all others named ‘N’) is equivalent in meaning to a description, which description? As Napoleon progressed from cradle to grave, did the meaning of his name continually change? When he won Austerlitz, did he also unknowingly change the meaning of his name? Saying that a name abbreviates a description at a time is of no avail, for surely the meaning of ‘Napoleon’ in 1769 was not ‘The Victor of Austerlitz in 1805’? Fourth, and conversely, people change their names (e.g. popes, women on marriage), but do they keep their meanings? If John Smith walks into a registry ofﬁce, and comes out Jack Jones, has he kept the meaning of his original name and attached it to his new one? Fifth, proper names and descriptions are not everywhere intersubstitutable. Not only can one not substitute a deﬁnite description for a signature, but further, one often cannot substitute a name for a deﬁnite description, e.g. in ‘The man who broke the bank at Monte Carlo last year did so again’. Further, Wittgenstein objected to Russell’s claim (cf. Exg. §79) that if a name is deﬁned by a description, and different people give different descriptions (or the same person gives different ‘deﬁnitions’) on different occasions, then, it

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seems, that name is ambiguous, and so is every sentence in which it occurs. Secondly, he remonstrated, no one would actually give such a Russellian equivalence. For if it turned out that the description of N one gave rendered one’s statement ‘ΦN’ false, one would normally simply give an alternative description. No deﬁnition of ‘N’ need be acknowledged as expressing what one means and understands by ‘N’. (The question of whether such explanations give the meaning of ‘N’ at all will be examined in section 7.)

3. Cluster theories of proper names Given some of the difﬁculties that arise out of the simple abbreviation theory, it was entirely natural that its advantages should be preserved by modiﬁcation within the same framework. Hence the cluster theory (inspired, as noted, by a misinterpretation of PI §79). The core idea consists in claiming that the meaning of a proper name ‘N’ is given by a cluster of identifying descriptions, such that if most (or a weighted proportion) are satisﬁed by a particular person, then ‘N’ refers to that person (i.e. that person is N). This seems to save part of the spirit of a descriptivist approach. It relaxes the demand for strict determinacy of sense, holds that mutual understanding admits of degrees, and admits that explanations given on an occasion by specifying a single identifying description are incomplete. Variants of the cluster theory can be constructed, exploiting two degrees of freedom. (i) It may take a social form; i.e. the cluster associated with the name ‘N’ may be the set of (overlapping) descriptions in terms of which the speakers in a community cash ‘N’. Alternatively, it may take an individualist form; i.e. a cluster may be deﬁned relative to each speaker, consisting of the alternative descriptions which he uses on various occasions in explaining ‘N’. (ii) It may introduce the cluster of descriptions for each name ‘N’ in a regimented form appropriate to a calculus: for example, assigning a weight to each member of the cluster and specifying values of the sum of the weights of the descriptions satisﬁed by X to function as thresholds for settling whether X is N. (This is wildly unrealistic.) Alternatively, it may take a looser form, demanding only that there be some internal connection between each name ‘N’ and some set of descriptions. The advantages of the cluster theory, viewed from the descriptivist perspective, are patent. Variability in the explanations of a name among speakers or, over time, with one speaker, does not entail that this name has multiple senses or meanings. Communication does rest on shared understanding whose extent is determined by reference to the degree of overlap of clusters of descriptions. The meaning of a name ‘N’ is associated with a complex means for determining its referent, since satisfying a certain proportion of the descriptions of the cluster is a condition for being N. (Hence the cluster theory shows how to extend Frege’s conception of sense (the ‘mode of presentation of a Bedeutung’)

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to singular referring expressions whose sense appears more or less indeterminate. There is a parallel extension for concept-words exploiting the notion of cluster concepts. The cluster theory, however, is not without defects. (i) It is too restrictive in several respects. First, explaining who N is need not take the form of specifying descriptions supposedly synonymous with ‘N’. It can often be done by pointing to N or to a picture of N. So, unless such explanations can be shown to fulﬁl their function only when transformed into descriptions, the cluster theory cannot be a complete account of (what is conceived to be) knowing the meaning of ‘N’. Secondly, explaining who N is need not consist in giving a true set of descriptions of N. A child’s explanation of who Christopher Columbus was, for example, might specify that he was the greatest Spanish navigator, who discovered North America, and that he sailed there in 1495. In spite of these falsehoods, we might well take the child to be asserting something about Columbus or asking a question about him. Thirdly, explaining who N is need not consist in giving a uniquely identifying description. In suitable circumstances an acceptable answer to ‘Who was Plato?’ might be ‘A great Greek philosopher’. What is required to establish that a person is speaking of N (‘knows what “N” means’) may vary with circumstances. What is accepted as a criterion here may be giving a description that falls far short of being uniquely identifying. Fourthly, explaining who N is by pointing to N or by giving a description of N is in many cases treated as a complete explanation of who N is and as a criterion for full knowledge of who N is (or what ‘N’ means). This is inconsistent with the guiding idea that the content of the cluster goes far beyond what is explicit in particular explanations. On that view, giving a particular explanation (short of a conjunction of all the descriptions in the cluster for N) would be only good inductive evidence for possessing full knowledge of what ‘N’ means. (ii) The cluster theory does not actually establish that there is a shared understanding of names. It does not succeed in showing that there is anything in common between two people each of whom uses the name ‘N’ to refer to N. According to the social version, only the investigator who has collected the data really knows the meaning of ‘N’. According to the individualist version the meaning of ‘N’ may vary from speaker to speaker, each person associating a different cluster of descriptions with a given name. (iii) Conceived as outlining an account of the meaning of proper names, the cluster theory contravenes the grammatical platitudes that meaning is the correlate of explanation, and that what is understood by an expression is what is explained by a generally acceptable explanation. In the calculus version, this is obvious. For explanations of who N is do not actually take the form of specifying a large cluster of deﬁnite descriptions together with a set of weightings and threshold values for being the referent of N. We do not explain names in this way, or apply them on these grounds (and for good reason). The same divorce of meaning, understanding and explanation holds for the looser

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version. For it, too, holds that what is given in ordinary explanations of who N is falls short of full speciﬁcation of the meaning of ‘N’, and hence too of what someone knows who knows the meaning of ‘N’. Furthermore, it concedes that explanations may take many forms, including pointing at N or at a portrait of N. Nevertheless, it insists that these explanations, whatever their surface form, determine the meaning of ‘N’ as given by certain deﬁnite descriptions that N satisﬁes. We may concede that one may explain who N is by pointing him out in a crowd. If the learner later misidentiﬁes N, one might criticize him by saying, ‘That’s not N; his hair is straight, but N’s is curly’. But this does not imply that one meant to convey by one’s ostensive explanation that N has curly hair and that the addressee understands one’s explanation only if he gathers this information from it, let alone that such descriptions are part of the meaning of N’s name. These criticisms of the cluster theory do not touch the more general question of whether proper names really do have a meaning that determines their referents. What they establish is that the cluster theory has non-trivial implications concerning the relationship of meaning to understanding and of understanding to explanation. This shifts the focus of debate to more general issues. It also opens up the possibility of making a fresh start on the discussion of proper names by applying some of the general principles gleaned from the Investigations.

4. Some general principles The key to a philosophical overview of the use of proper names lies in the different aspects of understanding names and sentences in which they occur. Light is shed on the roles of proper names by considering various ways in which one might misunderstand names in sentences. Wittgenstein never elaborated this, but it is in harmony with his conception of meaning, understanding and explanation. Understanding a token of ‘N’ as a name. Someone might not construe a token of ‘N’ as a name, even though it is used as one. One might wrongly take a use of ‘the Rocky Mountains’ to be a description, not realize that ‘If ’ is the name of Kipling’s poem, or fail to recognize a book title for what it is. Conversely, one might misconstrue a token of ‘N’ as a name even though it is not one. Some Puritans took ‘Moreover’ in ‘Moreover the dog licked his wounds’ as the dog’s name, and honoured the imaginary dog by naming their dogs accordingly. Understanding a name presupposes recognizing it as a name. That in turn requires knowledge of the manifold conventions concerning what is named and what stock of names is drawn upon for given types of objects in a particular language. Understanding the type-name ‘N’. Someone might not know what the name ‘Peter’ means (viz. ‘rock’), that the second component of ‘Leif Ericson’ is a

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patronymic, that ‘Vanya’ is a diminutive of ‘Ivan’, or that ‘Mathilda’ is a woman’s name. For many names there are such possibilities of failures in comprehension, some of which bear on knowing the use of the name (e.g. patronymic, diminutive) and others which do not (e.g. the meaning of ‘Peter’). Titles of many books, plays, operas, poems, etc. occupy a rather curious position, for many such names are not, qua type-expressions, generally employed as names (e.g. War and Peace, Wuthering Heights). Understanding, here, is complex. One must grasp the expression as the name of such a work of art, grasp the meaning of the title, and perhaps also understand the rationale of the name (read Much Ado about Nothing, then you will understand the title). For although the name does not determine its referent, its relation to its referent is not coincidental, and its connotative elements are often objects of understanding even if they do not determine the referent. Understanding how names are used. Someone might not understand the practice of using names to address messages, to call persons, as signatures to assume legal obligations, to honour people by naming places, or insects, or ﬂowers, after them, to commemorate the dead by writing their names on tombstones or war memorials, etc. Part of understanding a name is grasping at least the important elements in the institutions of name-using characteristic of the community to whose language the name belongs. Understanding to whom or what a token-name is used to refer. A person might not know, or might misidentify, to which S (where ‘S’ is a sortal) ‘N’ is used to refer. Doubtless the question ‘Who is N?’ or ‘Which N do you mean?’ are the most common questions that arise in this context. Because of our general command of all the facets of how to use names (in our society), our understanding of an utterance incorporating a particular name is commonly ﬁxed up to this last point: knowing for whom or what ‘N’ stands. Understanding the language-game in which a name is used referentially. A person might fail to grasp that ‘N’ is being used in the context of a story, or in a discussion of mythology, or in a religious context. The beginning of wisdom is recognition of the multiple aspects of understanding names. The second step is to note the complexity of the criteria severally linked with each of the aspects of understanding. This opens up the possibility of a critical, but conservative, reaction to the descriptive tradition. This conservative reaction is closest to Wittgenstein’s remarks about proper names. It leaves undisturbed three interrelated assumptions: (a) that names have meanings (Wittgenstein never hesitates on this); (b) that explaining who N is, is explaining the meaning of ‘N’; hence, (c) that names are typically ambiguous inasmuch as indeﬁnitely many people may bear the same name. Nevertheless, the conservative reaction stresses three signiﬁcant points missing from the traditional account. First, there are diverse aspects, quite distinct from reference, to understanding names and sentences in which they occur. Secondly, there are diverse criteria for knowing who N is which are compatible with mutual understanding. Equally, there are diverse criteria for understanding different

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practices and institutions of using names. Thirdly, the symptoms and criteria for understanding names, in particular of knowing who N is, may ﬂuctuate. Let us examine the criteria for understanding to which S ‘N’ (in a given utterance) refers. If we restrict ‘N’ to a person’s name, this is the question of the criteria for knowing who N is. The forms of explanation of who N is, and the criteria for knowing to whom ‘N’ refers, are diverse. There are different kinds of explanation of who N is: (i) Ostensive explanation: ‘That + is N.’ (ii) Locative explanation: ‘N is standing by the tree.’ (iii) Explanation by description: we give a description of N sufﬁcient in a particular context to identify N and distinguish him from others with whom he might be confused. Different descriptions may be appropriate in the same context, some descriptions may be useless in some contexts (e.g. a description of someone’s career will not help to identify him in a crowd (TS 211, 494)), and what is sufﬁcient in one context may be insufﬁcient or excessive in another. (As noted, in some contexts a uniquely identifying description is not necessary to determine satisfactorily for the purposes at hand who is meant (‘Who is Plato?’ — ‘A Greek philosopher’).) (iv) Explanation by another proper name: ‘Tully is Cicero.’ (v) Explanation by anaphoric pronoun (important in ﬁction): ‘A tall man was walking down the dark street . . . He was Sherlock Holmes.’ (vi) Explanation by introduction and self-introduction. (vii) Explanation by photographs and portraits. There is equal diversity in the criteria for understanding who N is, for example, giving a correct explanation of one kind or another, and using ‘N’ correctly. The internal diversity of the criterion of correct use is evident too — e.g. using ‘N’ to call N, to address him, to make statements about him, to give directions for ﬁnding him, to make a list of people who . . . , etc. Like the multiplicity of criteria for understanding an expression in general, the multiplicity of criteria for knowing who N is has important corollaries. Giving a correct explanation of who N is does not entail applying ‘N’ correctly. But it is important to our use of names that a person who correctly explains who N is generally goes on to use ‘N’ correctly. Nevertheless, this is a contingent regularity, and someone may be able to explain who N is, yet be unable to recognize or identify him. Giving a correct explanation of ‘N’ is a criterion for knowing who N is. Hence any explanation of who N is will be open to revision in the event of defeating evidence.2 The indeﬁnitely extendable possibility of revising such explanations of the names of other people is prominent in Wittgenstein’s account (PI §§79, 82, 87). Although defeasible, satisfaction of criteria for knowing who N is establishes, ceteris paribus, that a person knows who N is. The possibility of defeat by additional evidence does not demonstrate that the explanation is inadequate and needs completion (PI §87). 2

But not so in the case of one’s own name — one introduces oneself.

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5. Some critical consequences The strategy delineated bears on traditional approaches conducted on the basis of the same assumptions. (i) No-sense theories (e.g. Mill, Kripke) fail to provide for criteria of understanding. A person’s making any number of correct statements about N is accordingly compatible with his not knowing who N is. At best, whether someone knows who N is can be a more or less probable hypothesis. Nor is provision made for aspects of understanding names that do not pertain to knowing the reference of a name. (ii) Both abbreviation and cluster theories identify knowing who N is with knowing a rule stating necessary and sufﬁcient conditions for someone to be N. They confuse a defeasible criterion of knowing who N is with a sufﬁcient condition for being N, and conﬂate knowing who N is with knowing what ‘N’ means. (iii) The independence of the two kinds of criteria for knowing who N is reveals another misconception: that a person’s knowing who N is, where not manifested in his ability to specify necessary and sufﬁcient conditions for someone to be N, must consist in his implicit knowledge of such a rule. It is assumed that someone’s identiﬁcations of N must ﬂow from something — if not from a principle that he can state, then from one that he knows implicitly but cannot formulate. But the only ground for attributing such implicit knowledge is that the person applies ‘N’ correctly, and this is already a criterion for his knowing who N is. So the manoeuvre is redundant unless the reservoir conception of knowledge and understanding is correct (see Exg. §149, 2(iii), §150, 2.1(ii)). (iv) The variability of explanations of who N is seems tantamount to radical ambiguity of ‘N’ (Frege), unless these explanations are selections from a single, highly complex, hypothesized application rule (cluster theories). The horns of this dilemma are avoidable if giving any one of various explanations is viewed as a criterion of knowing who N is. This applies to names the general point that the multiplicity of criteria for understanding an expression does not entail multiplicity in what is understood. (v) Knowing who N is may be described as knowing how to identify N. This platitude may mislead. ‘Knowing how to identify N’ seems to legitimate the request for a justiﬁcation of any identiﬁcation of N. No doubt we can sometimes justify taking a person to be N. But if someone introduces himself by saying ‘I am N’, does it make sense to ask how he knows? Of someone with whom I live (wife, husband, parent, child), does it make sense to ask how I know who this person is? Must I always have a justiﬁcation for saying ‘That is N’? That there are criteria for a person’s knowing who N is — indeed, that a person can and does explain who N is — does not entail that his knowledge of who N is must be derivative knowledge. (vi) Recognition of the non-triviality of contingent identity-statements does not force us to embrace a descriptive theory. Giving some correct explanation

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of who A is, is a criterion for knowing who he is. Giving some correct explanation of who B is, is a criterion for knowing who he is. There is no inconsistency in attributing to someone knowledge of who A is and knowledge of who B is, yet denying that he knows that A is the same person as B. One does not have to know everything about A in order to be said to know who he is — in particular, what one may not have realized is that he is B. This is perfectly intelligible even though the names cannot be said to have a meaning that determines their reference. (vii) Similarly, the intelligibility of sentences incorporating ‘empty names’ does not entail the truth of a descriptive account. All that is required is that there be criteria for someone’s knowing who N is — a mythological hero, a god, a ﬁctional character, etc. Sentences in which the name ‘Sherlock Holmes’ occurs are not rendered meaningless just because no such person ever existed, and to clarify their meaning, it is not necessary to assume that an explanation of who Holmes was gives the meaning of that name. Furthermore, such an explanation cannot coherently be supposed to specify the conditions necessary and sufﬁcient for someone to be Holmes, which no one happens to satisfy. These considerations suggest that between no-sense theories and disguised description theories we are offered too few options. We may be well advised to begin afresh.

6. The signiﬁcance of proper names Philosophers in the twentieth century examined proper names almost exclusively as part of a ‘theory of singular reference’ within the framework of an endeavour to construct a philosophical semantics. The foregoing investigation suggests that giving an account of proper names boils down to elucidating criteria for understanding names and sentences in which names occur, and that such understanding has many aspects, each of which may give rise to different misunderstandings. Possession of a name. ‘Why should it not be possible that a man’s own name be sacred to him? Surely it is both the most important instrument given to him and also something like a piece of jewellery hung around his neck at birth’ (GB 125f.). Wittgenstein here stresses the enormous signiﬁcance in most cultures of having a name, and the importance we attribute to our name. Names, for us, are not mere referring devices, replaceable in principle by numerals. One could not say of prisoners’ numbers what Goethe said of persons’ names3 3 Goethe’s remark from Dichtung und Wahrheit is quoted in Exg. §171, 3. Cf. also Jean Valjean’s striking remark in Victor Hugo’s Les Misérables, V, vii, 1: ‘Fauchelevent may have lent me his name, but I have no right to use it. A name is an identity . . . To make use of a borrowed name is an act of dishonesty, as much a theft as to steal a purse or a watch. I cannot cheat decent people in that way — never, never, never! Better to suffer the tortures of the damned! And that is why I have told you all this.” He sighed and added a last word: “Once I stole a loaf of bread to stay alive; but now I cannot steal a name in order to go on living.’

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(MS 131, 141). Referring to a person (e.g. a prisoner) by a numeral rather than by his name is a form of degradation. We speak of bringing glory to our name, of making a name for ourselves in the world, of dishonouring our name or besmirching it, of having our name dragged through the mud. In certain circumstances a name is not only irreplaceable, but also has, as it were, a life of its own. The closest approximation to immortality is fame. A person ‘lives on’ after his death provided his name survives. Christians have held possession of a name (through baptism) necessary for salvation, hence the importance of christening infants immediately after birth or even before (e.g. ‘Vitalis’), lest they die nameless. The corollary of attaching importance to having a name is dread of losing it. Hence a severe form of punishment is deprivation of one’s name (e.g. outlawing some clan-names in eighteenth-century Scotland). Enforced allocation of new names from a select stock, as was common with slaves in the eighteenth century, reﬂects the attitude held towards the slaves. Even ‘harmless’ punning on a person’s name (as Herder on ‘Goethe’ (cf. Exg. §171, 3) is commonly felt to be peculiarly insulting and hurtful. In all these cases, the ‘signiﬁcance’ of a name extends far beyond its role as a singular referring expression. Somebody who did not understand this would betray at least a partial failure to understand names and their uses. For these features are not mere anthropological curiosities. They interlock with the form of life of a culture, and involve features of the correct use of proper names. Uses of names. The wider signiﬁcance of names is screened out by viewing them primarily as referring devices. (a) Names are used to label property (clothes), on door-bells, on tombstones and memorials, on signposts to show directions, on maps, and in numerous other ways. Knowing the use of a name involves far more (and in some ways far less) than knowing an unerring means for identifying its bearer on a given occasion of its use. (b) There are uses of a name such that it cannot be replaced by any other expression, not even by a deﬁnite description conceded to have the same reference. This is so in certain oaths, in the ceremony of swearing by one’s name, in signing a legal document, in staking a claim to a piece of property, in a marriage ceremony, etc. (c) There are prohibitions or restrictions on the use of a name by certain persons in certain circumstances, e.g. the use of pet-names, nicknames, forename or surname, maiden-name, name with or without title, etc., or the impermissibility in some societies of mentioning or using the name of a deceased person for a given length of time, or of A’s using B’s name if A stands in a certain kinship-relation to B. It is not obvious that this range of features, only a few of which are here mentioned, should be dismissed as ‘mere pragmatics’. Ubiquity. Most names are drawn from a relatively limited common stock; indeed, from common stocks — for there are different stocks of names for different kinds of things (e.g. ﬁrst names of males, of females, names of different kinds of pedigree animals, names of battleships). Naming, Wittgenstein noted, is rather like attaching a label to an object, perhaps like hanging the label ‘PORT’ on a decanter. In our linguistic cupboard, as it were, we have a

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store of names appropriate for different kinds of things. Allocating a name to the correct stock is part of understanding it, misallocating it a form of misunderstanding. ‘Mathilda’ is a woman’s name, not a man’s; ‘Fido’ is a dog’s name, not a person’s; and ‘Moreover’ is not a name at all. Taking ‘Mathilda’ as a man’s name is a criterion for failing to understand this name. (It has nothing to do with the ability to answer the question, ‘Who is Mathilda?’) This connotative aspect of proper names may be more or less rigid. Nothing prevents a person today from calling his son ‘Mathilda’. Name-giving not in accord with the ‘connotation’ of a name typically, with us, results merely in eccentricity. But it would have been impossible to christen a child ‘Beezebub’ or ‘Judas’ in medieval England. Etymology. The derivation of a proper name might seem of mere antiquarian interest — not a contribution, except by coincidence, to clarifying its meaning. But in the case of proper names this conclusion is mildly perverse. The question ‘What does “Peter” mean?’ has one (and only one) quite ordinary use, and the answer to it would be ‘rock’. Hence, what the descriptive theory dismisses from consideration is actually the only admissible answer to the question as ordinarily used and understood. (Other kinds of answer to ‘What does “N” mean?’ may be appropriate for other kinds of names, e.g. the seventeenthcentury Christian name ‘Original’, the book title Principia Mathematica, or the play title Back to Methuselah.) Of course, that is no coincidence. Philosophers’ interest in proper names has been guided by the thought that the meaning of a name must be what determines its reference, and must be its contribution to the meaning of any sentence in which it occurs. The meaning of a name, as naturally understood, plays no such role, and therefore is screened out. But this obscures the fact that there is much to understand about proper names and their use, and in some cases, for example in the case of book titles or titles of other works of art, the name may well have a meaning that is bound up with the character of the nominatum, even if it does not determine the reference. Name-giving. It would be misleading to treat name-giving as a straightforward species of stipulative deﬁnition. Baptism would then be likened to the ostensive deﬁnition of a new symbol. Every act of name-giving would be an autonomous linguistic activity, a preparation for the real business of using a name to refer to its bearer. This conception ignores the fact that there are typically principles restricting or necessitating the choice of a name from a common stock. Principles of restriction are obvious. At the least stringent end of the spectrum is our segregation of forenames into male and female names, or a ban on giving the same forenames to different living children of the same parents. More restrictive would be the practice of choosing a child’s name from among the forenames of deceased ancestors, or limiting certain names to the eldest child (e.g. ‘Original’) or to twins. Even more restrictive would be the practice of selecting names from a limited stock with the proviso that the chosen name must not already be owned by a living member of the society. Here, if the stock were meagre, a child might have to wait for a name, perhaps

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without any right to refuse the ﬁrst vacated name offered. Here principles of restriction collapse into principles of necessitation. These too are familiar. In a name system incorporating patronymics, nobody can choose his or another’s patronymic. The father’s death may pre-ordain the name (‘Posthumus’ or ‘Posthuma’). In certain systems of necronyms or technonyms a person’s name, or part of it, is predetermined by principles for allocation (and change) of name. The more prominent, institutionalized and stringent the principles governing the selection of names, the more name-giving will be constrained by a common practice of name-allocation, and may itself display understanding, misunderstanding or lack of understanding. Equally, the more relevant to understanding the name will be its connotative aspects. In a name system where each person has a forename, middle name and surname, each restricted or perhaps necessitated by different conventions, there is much to understand in bestowing names upon a child, and much to be understood from the mere name of an adult. Deviant (attempted) name-giving may be a criterion of misunderstanding the name. Equally, failure to realize that a person’s middle name signiﬁes his father’s or mother’s lineage, his totem or tribe, his relationship to a signiﬁcant object or person, etc. will also show a form of misunderstanding. This may be reﬂected in many ways, e.g. asking closed questions or making self-contradictory assertions. Complexity. Names are held to be unanalysable or simple. They are not understood in virtue of understanding their parts (if any). Apparent counterexamples are circumvented by appeal to a counterfactual: e.g. that this road (person) might still be called ‘Oxford Road’ (‘Harold Godwinson’) even if it were impassable to trafﬁc and no longer led to Oxford (even if he were not Godwin’s son). Hence it is inferred that the constituents of a name are (i) irrelevant to understanding it, and (ii) do not have any role in determining its referent, because there are possible circumstances in which they would not do so. This conclusion is unwarranted (and embodies a pattern of reasoning against which Wittgenstein argues). That some things might not, in changed circumstances, fulﬁl a certain role (e.g. samples, methods of measurement and calculation) does not prove that they do not, in existing circumstances. This mistaken reasoning rests on two assumptions about names. First, only questions concerning reference-determination are relevant to understanding a name. Hence knowing how to determine its reference amounts to complete understanding. Would someone lacking knowledge of the system of Roman nomenclature, who was told ‘That + is Marcus Tullius Cicero’, have a full understanding of this name, know its use (e.g. how to address its bearer)? Anglo-Saxons commonly ﬁnd Russian novels bewildering because they do not understand the Russian name system of patronymics, diminutives, etc. As noted above, in many name systems the complexity is genuine — different constituents are governed by different principles of selection and make distinctive contributions to the name, and so involve distinct criteria of understanding. Secondly, it is assumed that what is understood in understanding a name ‘N’ must be

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given by a rule specifying necessary and sufﬁcient conditions for being N. This is what gives room for the counterfactual argument: e.g. being Godwin’s son is not a logically necessary condition of being Harold Godwinson, so not part of what is understood in understanding the name. But there are criteria for understanding a name ‘N’ and the system of nomenclature to which it belongs, even though what is understood may not, and usually does not, consist of conditions necessary and sufﬁcient for being N. Secondary reference. There is a strong temptation to speak of multiple reference in the case of allusive use of proper names of historical ﬁgures in ﬁction. An account in terms of different degrees or depth of understanding is preferable. There is no simple answer to the question whether ‘Mozart’ in Mörike’s novella refers to the composer. But clearly one would not fully understand this work if one knew nothing about the composer or failed to relate one’s knowledge to the central ﬁgure in Mozart’s Journey to Prague. Discussion of such allusions calls for sensitive judgement. The question ‘What is the reference of “N”?’ is an inappropriate vehicle for such discussion, whereas ‘What is involved in correct understanding of particular sentences incorporating “N”?’ is more fruitful. Empty names. In connection with names, philosophical logicians suffer from a horror vacui. It results, again, from conceiving of names exclusively as referring devices and of understanding them as being exhausted by knowing the means of reference-determination. The multiple forms of so-called referencefailure must be examined separately, for they are severally distinctive. But none of them (ﬁction, fable, myth, jokes, pagan deities, etc.) threatens treating such an expression as a genuine proper name. The classiﬁcation of an expression as a proper name should not depend on the factual question of whether it has a bearer that exists or existed. One important aspect of distortion concerns knowing who N is in such cases. One strategy equates knowing who N is with knowing the meaning of ‘N’, i.e. knowing a means of identifying N. What is known and understood is the sense of ‘N’, and this, together with the facts, will secure reference for ‘N’. In the case of empty names, what we know is what would have to be the case for ‘N’ to secure reference, and hence for any sentence containing ‘N’ to be true. But what would ‘have to be the case’ for ‘Zeus’ to ‘secure reference’, or ‘Pegasus’, ‘Sherlock Holmes’ or ‘Kilroy’? Surely the answer is that no set of facts would establish that someone was Sherlock Holmes, or that some horse was Pegasus. Yet any reader of Conan Doyle can say who Sherlock Holmes is. A related misconception is the thought that such names lack reference, that in speaking of Sherlock Holmes or of Pegasus, one is not referring to anything. But that is surely perverse. For the question ‘Who is Sherlock Holmes (Pegasus)?’ or ‘Who are you talking about?’ has a straightforward answer, even though it is true that no such person (or winged horse) ever existed. (It would be equally perverse to suppose that there are no true statements about Holmes.)

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Timelessness of reference. The practical adoption of this allegedly anodyne convention by a person would manifest a form of misunderstanding of names and their use. After Miss Smith has married Mr Jones, she is (or, now, typically is) Mrs Jones, not Miss Smith. Nor need her previous name remain ‘vacated’. In eighteenth-century England ‘Miss Smith’ would be used to designate the eldest unmarried daughter of the Smith family, so that a younger sister would assume this name as soon as the next older one ‘vacated’ it. To persist in using ‘Miss Smith’ to refer to Mrs Jones would be a mistake or an insult. This is even more obvious and incontrovertible in name systems involving necronyms or technonyms. So too in cases of religious conversion (e.g. Paul and Abraham), adoption or the medieval practice of allocating a new name on conﬁrmation in special cases (Archbishop Peckham’s ruling: the person’s name before God and in law is (thenceforth) that conferred at conﬁrmation in such cases). All these aspects of proper names have been marginalized or ignored in philosophical discussions of proper names over the last century. Looking at names from the viewpoint of criteria of understanding can remedy this defect. Proper names are importantly unlike arbitrary signs or index numbers. A community whose language contained no expressions comparable to proper names in their ramifying signiﬁcance would have a way of life and thought very different from ours.

7. Proper names and meaning It is time to face the question of whether names have a meaning that determines their referent at all. Frege’s reﬂections were moulded by his commitment to his distinction between sense (Sinn) and meaning (Bedeutung). This distinction, rooted in requirements of his function-theoretic apparatus and his logicist programme, arguably distorted his description of the linguistic phenomena. He had at least ﬁve reasons for ascribing what he called ‘sense’ to names. (i) To explain how a sentence of the form ‘ΦA’ has a sense. That the sentence as a whole has a sense seemed evident, since the sense of a sentence is the thought (proposition) it expresses. Assuming that the sentence splits up into argument-expression and function-name, and that the sense of the sentence is composed of the senses of its constituents, then a proper name must have a sense that both determines its referent and is part of the thought. (ii) To explain the difference in sense between ‘ΦA’ and ‘ΦB’. For, to be sure, the referents of ‘A’ and of ‘B’ are not part of the thoughts expressed respectively by ‘ΦA’ and ‘ΦB’. (How could Mont Blanc with all its snow-ﬁelds be part of the thought that Mont Blanc is 4,808 metres high?) So what differentiates the two thoughts must be the senses of the respective names. (iii) To explain the informativeness of non-trivial identity-statements — for if ‘A’ and ‘B’ lack any sense, it seems that there can be no difference between

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‘A = B’ and ‘A = A’. But that is absurd, since ‘Cicero is Cicero’ is uninformative, whereas ‘Cicero is Tully’ may convey new knowledge. (iv) To explain how we can understand a sentence containing an empty name, e.g. Odysseus landed in Ithaca’. For, since ‘Odysseus’ does not stand for anything, then if it also has no sense, how can there be anything to understand? (v) To provide a ‘mechanism of reference’ (a means of determining a referent (a Bedeutung)) that will simultaneously explain the contribution of a name to the sense of a sentence and provide the content of understanding when names (and sentences containing them) are understood. Wittgenstein too speaks freely of the meanings of proper names. He rightly objects to Frege’s misuse of ‘Bedeutung’ in taking the bearer of the name to be the Bedeutung of the name, and distinguishes the meaning of a name from its bearer (PI §§40 –3). He points out that the meaning of a name is sometimes explained ostensively (PI §43), and speaks of deﬁning the name ‘N’ (PI §79). But this too is misconceived. We may start with some common-or-garden hesitations. The only use we give to such questions as ‘What does “Peter” mean?’ is as requests for explanations of the etymology or derivation of such a name. (Further reﬁnements are necessary for other kinds of names, e.g. place-names and titles of books, songs, plays, etc.) We do not ask ‘What does “Napoleon” mean?’ (except in the above sense), but rather, ‘Who was Napoleon?’ Still less do we ask, when we do not know who is being talked about, ‘What does the name “John” mean?’, but rather, ‘Who is John?’ or ‘Which John do you mean?’ or even ‘John who?’ (answered by e.g. ‘John Smith’ or ‘John, the plumber’). We do not treat such answers as explanations of the meaning of ‘John’, although they may be partial explanations of what was meant in saying ‘John called this morning’. We speak of different persons bearing the same name, and would be unsurprised to learn that in 1899 there were two Winston Churchills (one an ambitious young British ofﬁcer, the other an American novelist),4 but we should be bewildered if told that each one’s name had a quite different meaning from the other’s. If we do not understand an assertion ‘ΦN’ because we do not know who N is, that is what we would say — not: ‘I don’t know the meaning of “N”’ or ‘I don’t understand what the name “N” means’. These humble considerations may be reinforced by examining some of the consequences of philosophical attributions of meaning or sense to individuals’ names. Frege must embrace the thesis that there are as many senses of the expression ‘John Smith’ as there are people called ‘John Smith’, because, in his view, the sense of a name determines what it stands for. (In fact, he is committed to even more radical ambiguity, since each John Smith’s name has, or may have, different senses attached to it by different speakers.) Wittgenstein seems to be committed to a similarly implausible view, since on his account 4 For the amusing exchange of letters, see W. S. Churchill, My Early Life (Fontana, London, 1959), pp. 223ff.

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each John Smith will have a name with a different ﬂuctuating and indeterminate meaning. This ambiguity thesis is a distortion of the familiar fact that many people, places, pets, etc. share the same name. It also distorts the very notion of ambiguity. Ambiguity of words is a local, language-speciﬁc feature, not commonly preserved in translation into a different language, never in translations into numerous other languages.5 So names are not, in any ordinary sense, ambiguous. It is an important datum that people may share the same name, and absurd to conceive of N.N. père saying to N.N. ﬁls, ‘I have given you my name, but not its meaning’. ‘Mr White is white’ is a case of ambiguity (compare translations of it); ‘Mr White the plumber and Mr White the joiner both . . .’ is not. Do we need to attribute meaning (understood as determinant of reference) to a particular person’s name even for the purposes of explaining the features that concerned Frege? (i) One can explain what is meant by the utterance of a sentence ‘ΦA’ without attributing a meaning to ‘A’. It is the misguided commitment to the idea that the meaning (or sense) of a sentence is composed of the meanings (or senses) of its constituents that makes this conclusion compelling. But there is no good reason to accept such compositionalism. To understand what is said by the utterance of such a sentence as ‘ΦA’, one needs to know who A is, but that does not require knowing a means of identifying A that is constitutive of the meaning of the name. (ii) Consequently, one can explain any difference in meaning between ‘ΦA’ and ‘ΦB’ without attributing it to the different meanings of ‘A’ and ‘B’. In so far as ‘ΦA’ differs in meaning from ‘ΦB’, that is manifest in the explanations of these two sentences (in a given context) which are accepted as correct. But no such explanation requires ascribing meanings to ‘A’ and ‘B’. (iii) The informativeness of non-trivial identity-statements does not require attributing senses or meanings severally to ‘A’ and ‘B’ (where A = B), as long as it is intelligible that one know who A is and know who B is without knowing that A is the same person as B. This surely is perfectly intelligible. To know who A is, is manifested by giving some appropriate answer to the question ‘Who is A?’, but does not require knowing every correct answer to it. (iv) The intelligibility of a sentence containing an empty name is likewise unproblematic, as long as there is a correct answer to the question ‘Who is N?’ It is perfectly possible to answer questions such as ‘Who is David Copperﬁeld (Zeus, Kilroy, Odysseus)?’ even though, in one sense, these names lack a bearer. Indeed, it is misguided to assume that sentences containing 5

However, names do belong to a language; ‘Peter’ is an English name, ‘Pierre’ a French one. But Giuseppe Verdi isn’t Joe Green. Nevertheless, Jerusalem is Yerushalayim and Rome is Roma. Is this translation? Or should one rather say that ‘Jerusalem’ and, ‘Rome’, are the English versions of the Hebrew and Italian names?

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them are uniformly truth-valueless. This stems from applying the standards of one language-game to another, rather different one. (v) There is no mechanism of reference. There is, rather, a practice of using names in various contexts, inter alia to refer to people, and a practice of explaining who, in a given context, is referred to by a particular name. Objectivity of reference is secured because the existence of a practice of explaining who was referred to by ‘N’ in a particular utterance ‘ΦN’ ensures a distinction between believing that ‘N’ refers to so-and-so (e.g. to that + person) and ‘N’ ’s being used, in a given context, to refer to him. It is not necessary to assume that names have meanings that determine their reference. Traditional accounts of their meaning have unwelcome consequences. So we can now jettison the three dogmas left undisturbed by the conservative reaction: i.e. that names have meaning (in the preferred sense), that explaining who N is, is explaining the meaning of ‘N’, and therefore that names are typically polysemic. If we jettison the assumption that names have meanings that identify their bearer, then there can be no such thing as explaining their meaning. What is misdescribed as ‘an ostensive deﬁnition’ of the name ‘N’ is not an explanation of the meaning of ‘N’, but an ostensive explanation of who N is (relative to a particular utterance). Of course, the name ‘N’ may be uttered as a oneword sentence (vocatively, assertorically or interrogatively), and this utterance can be explained. But an explanation of what is meant by a one-word tokensentence is not an explanation of the meaning of its constituent. The possibility of explaining what is meant by the one-word sentence-token does not entail that the name ‘N’ has a meaning; nor does denying meaning to the name imply that the sentence is meaningless. Moreover, although in N’s presence one can replace ‘N’ in ‘N is tall’ by ‘He + is tall’, it does not follow that ‘N’ therefore has a meaning, but only that the two statements say the same. One and the same name may, but need not, have many bearers. This truism does not imply that names are polysemic. All it implies is that one must know who (which N) is being referred to in an utterance ‘ΦN’ in order to understand what statement is made. The analogies and disanalogies between proper names and indexicals or demonstratives are instructive here. In both cases there is something to understand: namely, a grasp of the conventions concerning the type-expression. In the case of the demonstrative ‘this’, if one understands the general conventions concerning the use of ‘this’ and one knows the context of an assertion ‘Φ (this +)’, then one is in a position to explain the meaning of the assertion and what object is referred to by this use of the demonstrative. Knowledge of the conventions for the use of ‘this’, together with relevant knowledge of the context of its use in an utterance, sufﬁce for knowing what that token of ‘this’ refers to and hence its contribution to determining what is said by the utterance of the sentence. As with such context-dependent expressions, so too with proper names we must distinguish the general rules concerning the use of the expression

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(whether it is a man’s name, a diminutive, a patronymic, a nickname, etc.) from knowing who or what is referred to in a particular utterance incorporating the expression. That I do not understand what statement is made by an utterance ‘Φ ( John)’ because I do not know who, in this utterance, is meant, does not imply that I do not understand the conventions governing the use of the type-name ‘John’ (that, e.g., it is an English male forename). An explanation of who is meant is no contribution to my grasp of the use of the name in general, but merely part of an explanation of the particular utterance — namely, who is being referred to. A fortiori, my ignorance of who else bears this name is not ignorance of other meanings of the name. Unlike indexicals and demonstratives, however, proper names are not context-dependent. An aspect of grasping the use of the former is knowing how their reference in an utterance is determined by the context of the utterance (time, place, speaker, etc.). Not so with proper names: there is no general systematic relation with the context of utterance such that one can determine from the general conventions concerning the type-name together with the context what the reference of ‘A’ is in an utterance ‘ΦA’. What one needs to know is simply which S is being spoken of, or who A is, or who is meant. And this one must know, whether ‘A’ has many bearers or only one. Even if the system of nomenclature and name-bestowal and the internal complexity of a given proper name together are such that an explanation of the typename sufﬁces uniquely to determine its bearer (e.g. that only the eldest son of X can be named ‘N’), giving this explanation of the name may not count as giving an explanation of who N is and hence may fail to qualify as a criterion for knowing who is spoken of. Although it is true that John D. Rockefeller III is the son of John D. Rockefeller Jr, such a statement is typically not an acceptable answer to ‘Who is . . . ?’, although it manifests understanding of an aspect of a naming system. The multiple features of understanding names elaborated above do not satisfy the requirements which the Fregean tradition demands of the meaning of a proper name: namely, a means of reference-determination, a content of shared understanding which will display the contribution of the name to the meaning of (or what is meant by) any assertion in which it occurs. Understanding sentences incorporating names commonly involves grasping various facets of the practice of using names, i.e. understanding their ‘signiﬁcance’. Failure to understand these aspects of name-use leads to incorrect uses of names, improprieties, incorrect explanations of, inappropriate utterances of, or improper reactions to, sentences incorporating names. These constitute criteria for misunderstanding or not understanding such sentences. But only a misguided commitment to compositionalism seems to force the conclusion that proper names have a meaning of which these various dimensions of signiﬁcance are a part. Indeed, there is no need for this. There are various rule-governed practices of name-use. These can be explained. There are criteria for understanding sentences incorporating names, criteria which sometimes involve reference

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to the background practices of using names. These criteria can be described. Once this is done, is there anything left that has not been explained? Is there any signiﬁcant feature about the use of names and the explanation and understanding of sentences incorporating them that has not been mentioned? Only the insistent demands of a dogmatic theory. Then it is this that must be subjected to criticism.

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

XIII

Turning the examination around: the recantation of a metaphysician 1. Reorienting the investigation Augustine’s picture of language constitutes the mis-en-scène for the Investigations. Its ramiﬁcations are sketched in §§1–27(a). The confusions of atomism, with its misconceptions of logically proper names, simple objects and complexes, of a ‘connection between language and reality’, and of analysis, are anatomized in §§27(b)–64. §§65–88 investigate misconceived demands on concept-words and their explanation: e.g. that they be deﬁned by characteristic marks, that they be everywhere circumscribed by rules, that the rules for their use budget for every possible eventuality. These misconceptions are rooted in misconstruals of meaning something by an expression and of understanding an expression, misconceptions about the relationship between explanations, grasping the use of an expression, and knowing what it means. These, in turn, are rooted in misunderstandings of the nature and role of logic. Frege and Russell had conceived of their calculi as logically perfect languages. Natural languages, they thought, fall short of such an ideal. Wittgenstein himself had thought of logic as the depth grammar of any possible language, for, he insisted, any language in which sense is expressed — in which something is meant — is logically in order as it is (for logic is a condition of sense), and will be shown to be so on analysis. In §§89–133, Wittgenstein turns to examine what had led him to misconstrue the role of logic and to assign to the logical investigations that seemed to be the concern of philosophy the sublime task of disclosing the essence of the world. This leads naturally to a discussion of philosophical methodology. These remarks constitute the deﬁnitive statement of Wittgenstein’s conception of philosophy and its nature, its pitfalls and proper path. The remarks fall (very roughly) into two groups, §§89–108(a) and §§108(b)–133. Although the Tractatus is barely mentioned (only in §§97 and 114), its presence is everywhere felt, and its misconceptions are under constant scrutiny in §§89–108(a). By contrast with the sequel (§§108(b)–133), which was written for the most part1 in the early 1930s and cannibalized from The Big Typescript, these remarks were written in 1937 speciﬁcally for incorporation into the 1

But not PI §§112–15.

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Early Draft. So they constitute Wittgenstein’s ﬁnal reﬂections on the methodological sins of the Tractatus. They diagnose what had been awry with his conception of the task of philosophy and with his philosophical method. Wittgenstein held those misconceptions to be not personal idiosyncrasies, but characteristic philosophical temptations and tendencies. When he completed the Tractatus, he believed that he had solved the fundamental problems of philosophy (TLP, Preface). Now, ‘forced to recognize grave mistakes in what I wrote in that ﬁrst book’ (PI, Preface), he thought of its misconceptions as exemplary. Small wonder that he wanted to publish his old thoughts and the new ones together, and held that the latter could be seen aright only by contrast with and against the background of his old way of thinking (ibid.). Reﬂecting afresh on his earlier conception, it became clear to him that the whole examination needed to be turned around,2 but about the pivotal point of our real need (PI §108). This is a dark remark. What counts as turning our examination around? And what is ‘our real need’? This rotation will, Wittgenstein writes, rid us of our misguided preconception of the ‘crystalline purity’ of logic — but what precisely he means by ‘logic’ here needs to be clariﬁed. Exactly what preconception of crystalline purity he had in mind must be pinned down. Ridding us of this preconception, he avers, will enable us to see that the rigour of logic is not in any way compromised by the realization that the concepts of language and of proposition are family-resemblance concepts. But to understand this observation, we must be clear why the familyresemblance character of these concepts might appear to compromise logic. For this we must apprehend what role Wittgenstein allocated to logic in the Tractatus, and why that was misconceived. Interestingly, in his notes (MS 157a, 48v) he observed that even if the concept of language were not a familyresemblance concept, his present conception would still be different from that of the Tractatus. So although acknowledging the family character of language is important, it is still not the crucial matter vis-à-vis this radical transformation in our way of thinking that is being advocated. So what is? This essay will attempt to answer these questions. It will show that rotating the investigation involves abandoning the ‘sublime’ conception of logic that characterized the Tractatus. That in turn implies desisting from ‘sublimating’ concepts such as ‘name’, ‘proposition’, ‘language’, and bringing such words (as well as their correlates, ‘object’, ‘fact’, ‘world’) back from their metaphysical to their everyday use. Above all, it involves abandoning the metaphysical aspirations of investigating an objective essence3 of the world by means of a 2

The translation of ‘Die Betrachtung muss gedreht werden’ is difﬁcult. ‘Betrachten’ is ‘to consider’, ‘Betrachtungsweise’ is ‘way of looking’ or ‘way of thinking’, but there is no straightforward equivalent of the nominal. I shall follow Anscombe’s ‘turning the examination around’, or, occasionally, ‘turning the investigation around’. 3 By contrast with the de dictu conception of essence endorsed in Investigations §§92, 371, 373. Note that the endorsement of §92 must not be seen as conﬂicting with Wittgenstein’s insistence that the concept of language is a family-resemblance concept.

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logical investigation, and relinquishing the very conception of such an a priori order of things mirrored in logic and discoverable by depth analysis.

2. The sublime vision Wittgenstein’s discussion of philosophy in the Investigations opens with the question: to what extent is logic something sublime? There seemed to pertain to logic a special depth, a universal signiﬁcance. It appeared to lie at the foundation of all sciences, and logical investigation seemed to explore the essence of all things (PI §89). This was the vision (strictly speaking, the ineffable vision) of the young Wittgenstein. In the ‘Dictation to Moore’ he claimed that ‘Logical so-called propositions show [the] logical properties of language and therefore of [the] universe’ (but, ‘it is impossible to say what these properties are’).4 Furthermore, ‘Every real proposition shows something . . . about the Universe’, he added, ‘. . . if it has a sense, it mirrors some logical property of the Universe’ (NB 108). In the Notebooks he wrote, ‘My whole task consists in explaining the nature of the proposition . . . in giving the nature of all being’ (emphasis added), a task that was to be executed by investigating logic, since ‘the allembracing world-mirroring logic . . . form[s] one inﬁnitely ﬁne network, . . . the great mirror’ in which the essence of the world is reﬂected (NB 39). Six months later, he noted that ‘the great problem round which everything I write turns is: Is there an order in the world a priori, and if so what does it consist in?’ (NB 53), and he subsequently concluded that there cannot be either an orderly or a disorderly world; rather, ‘In every possible world there is an order even if it is a complicated one’ (NB 83). His work, he wrote in 1916, ‘has extended from the foundations of logic to the essence of the world’ (NB 79). These aspirations are evident in the Tractatus itself — not only in the metaphysical or ontological remarks with which the book opens, but, even more importantly for our present investigation, also in the remarks on logic towards the end of the book. That the propositions of logic are tautologies, he concluded, shows the formal — logical — properties of language and the world (TLP 6.12). The propositions of logic represent the scaffolding of the world (TLP 6.124), and logic itself is a mirror-image of the world (TLP 6.13). This was a metaphysical vision par excellence: the world had an essential nature, which could be uncovered only by logical analysis; logic — that is, the logical forms of thought and language — represented the a priori order of the world, the order of possibilities common to both thought and the world, the forms of all things. What was unique about this vision were the claims that logic — the logic of language — mirrors the metaphysical properties of the 4

‘In order that you should have a language which can express or say everything that can be said, this language must have certain properties; and when this is the case, that it has them can no longer be said in that language or any language’ (NB 108). This constraint is determined by the bipolarity requirement on propositions with sense. Consequently essences cannot be described.

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world, and hence that logical (or logico-linguistic) investigation explores the essence of all things, and that what is thus inevitably shown in language cannot be said by means of language. So conceived, logical investigation was indeed sublime. But this sublimity was purchased with illusion and distortion. For, as Wittgenstein realized in his 1937 criticisms, the crystalline quality of logic, understood as the mirror-image of the world, was premissed on the supposition that a proposition must do something remarkable (PI §93). It must represent a state of affairs (even if it does not exist); it must describe a possibility available to the world (even if it does not obtain). It must not fall short of the fact that makes it true, and yet it must be distinct from the fact that makes it true. For it must describe what is the case if it is true, and what is not the case if it is false (PI §§428f.). The essence of language was hidden. It was buried beneath the surface grammar of natural language, and it was no good ‘simply to look and see’ how language functions (cf. PI §93). For the way it functions was not open to view. Only logical analysis, which had barely begun (RLF 163), could reveal what was thus concealed. What logic demanded (TLP 6.124) was that names (‘real names’) have meaning and elementary propositions have sense. But the real names and their logical forms were unknown and awaited analysis (‘in a certain sense a posteriori’ (RLF 163)). Their meanings were held to be simple objects that constitute the substance of the world. Elementary propositions were not the familiar sentences of daily discourse, but rather were the end-product of analysis into logically independent propositions each consisting of simple names concatenated in a fact. These propositions had a determinate sense. The sense of a proposition is its agreement and disagreement with the obtaining and non-obtaining of states of affairs. Every elementary proposition is a picture in the following sense: it depicts a possible arrangement of things, and, if asserted, says that this is how things are. Hence the general propositional form, shared by all propositions with a sense, is ‘Things are thus-and-so’ (or ‘This is how things stand’). Indeed, all propositions are pictures. Molecular propositions, being composed of elementary propositions, depict possible combinations of the obtaining and non-obtaining of elementary states of affairs. With this apparatus (and this abstract vision of what the world consists of ), Wittgenstein had been able to give an account of the essence of language, of propositions, of names, also of the essence of thinking, of the intentionality of thought and language, and of the essence of the propositions of logic and of logical relations. For propositions to do the remarkable thing they do, they must share a common form with what they depict (otherwise logic would not be ‘the great mirror’) — and they can do so because they are composed of, and are truth-functions of, logically independent elementary propositions. These in turn are facts that represent states of affairs, and are composed of names that share a common form with their meanings. Propositions must reach right up to reality, no matter whether they are true or false. Otherwise the false proposition could not, so to speak, depict how things are not, while still

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having the same sense it would have if it were true (cf. NB 30; PI §429). And this is ensured by the simple names of which the proposition consists having simple objects as their meanings, given that the names and the objects have common forms. Propositions must have a determinate sense, thereby excluding vagueness and reference-failure,5 otherwise they would not be subject to the laws of logic. And this too is ensured by the constitution of elementary propositions. For each elementary proposition divides logical space precisely into two, and is bipolar. So any vagueness in propositions of surface grammar is merely apparent, and disappears on analysis into disjunctions of determinate possibilities, while any apparent reference-failure in surface grammar disappears by modiﬁed Russellian analysis (Theory of Descriptions without identity). All propositions must be truth-functions of elementary propositions; otherwise, one could not display all logical relations as consequences of the inner truthfunctional complexity of non-elementary propositions, or claim that the limits of language coincide with the limits of the world. There was an array of hidden presuppositions seemingly required by this sublime conception in order to explain how the proposition can do the remarkable thing it does. These presuppositions concerned the apparent processes of understanding and thinking. These go virtually unmentioned in the Tractatus because they seemed to be of no concern to logic (TLP 4.1121). For the Tractatus — the Logisch-philosophische Abhandlung — is, above all, a treatise on logic. It answered the age-old question of the nature of logical truth and investigated the formal properties of the proposition. But there is a psychological hinterland (a mythology of psychology, as he later called it) implicit in the account of the intentionality of the proposition, in particular in the explanation of how the proposition can be false yet meaningful.6 It is explicit in the Notebooks 1914–16 and in the manuscript writings of the early 1930s. The intentionality of language was dependent upon the intentionality of thought (of meaning, intending), for the method of projection of a proposition was conceived to be thinking its sense, i.e. meaning by the proposition the state of affairs the obtaining of which makes it true.7 Names ‘reach right up to reality’ inasmuch 5

That the substance of the world consists of simple sempiternal objects ensured both. Logic, he held, presupposes that much (TLP 6.124). 6 Only in the 1930s did Wittgenstein discuss the very same problems of intentionality in terms of the intentionality of thought, belief and expectation rather than in terms of the problem of negation and the false proposition. For detailed examination, see ‘Intentionality’ in the paperback edition of Volume 4, Part I. 7 See TLP 3.11; PT 3.1–3.15. Note that both are mistranslated: ‘das Denken des Satz-Sinnes’ is ‘thinking the sense of the proposition’, not ‘thinking of the sense of the proposition’. In the Notebooks, see the discussion of meaning something by a sentence or word (meinen) on pp. 67f. and 70. In the early 1930s, see especially MS 108 (Vol. III), 218f.: ‘One could say, the intention is the method of projection. The picture (in the narrower sense) does not sufﬁce because how it is to be compared with reality is not given with it. Together with it must be the method of projection; but then the picture indeed reaches right into the place where the object of the picture is.’ See also MS 145, 49, quoted in Exg. §95 n., and PR 65.

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as in any use of a name in a sentence with a sense, the speaker means by the name ‘N’ the object N that is its meaning. This is of the greatest importance, not only because it is integral to Wittgenstein’s struggles with intentionality (i.e. the picture theory) and explains his later obsessive preoccupation with misconceptions about meaning something (see Volume 4, ‘The mythology of meaning something’), but also because given that depth grammar is hidden and altogether different from what appears on the surface of language, it must have some ‘psychological reality’. The young Wittgenstein, unlike philosophers ﬁfty years later, was not engaged in constructing a theory of meaning that will deliver the truth-conditions of any well-formed sentence from axioms, formation- and transformation-rules of a natural language independently of any psychological assumptions about speakers. He was accounting for the inner nature and essence of representation by means of language, and language represents only inasmuch as it is understood and meant. He thought that what gives an array of signs the status of a representation of how things are is using (or, in the case of the hearer, interpreting) the array to mean what is represented: namely, a possible situation. The processes of understanding a sentence, thinking its sense, interpreting it, must, it seemed, somehow contain the complete analysis of the proposition. With hindsight, of course, this was not so much a psychological presupposition as a metapsychological one — a profound confusion concerning the concepts of thinking (meaning) the sense of a sentence and understanding (interpreting) it, which it was to take Wittgenstein years to destroy. As he was later to write: All this, however, can only appear in the right light when one has attained greater clarity about the concepts of understanding, meaning and thinking. For then it will become clear what can lead us (and did lead me) to think that if anyone utters a sentence and means or understands it he is operating a calculus according to deﬁnite rules. (PI §81)

3. Diagnosis: projecting the mode of representation on to what is represented In 1929 the Tractatus vision disintegrated. There is no reason to suppose that when Wittgenstein returned to philosophy, he envisaged destroying his ﬁrst philosophy. He went to Cambridge, he wrote to Schlick, in order to work on perceptual space and other things.8 There is every reason to suppose that his idea was to turn from the problems of logic, which he had settled in the Tractatus to his satisfaction, to problems of the application of logic, to the analysis of the internal forms and contents of elementary propositions, which had deliberately been excluded from the Tractatus (TLP 5.557). He had barely begun 8

The ‘other things’ presumably were problems in the philosophy of mathematics.

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to work on this task when he ran into difﬁculties, which took the form of determinate exclusion (e.g. colour incompatibility), superﬁcially brushed aside in the Tractatus, and now clearly problematic (RLF; PR ch. VIII). From this seemingly insigniﬁcant little thread left dangling in the book, the whole tapestry of the Tractatus unravelled. The beginnings of a fundamental reorientation of his conception of philosophy, its forms and limits, took place remarkably quickly. By January 1932 he was writing: ‘Meine Hauptdenkbewegung ist heute eine ganz andere als vor 15–20 Jahren. Und das ist ähnlich, wie wenn ein Maler von einer Richtung zu einer andern übergeht’ (‘My main movement of thought is currently completely different from 15–20 years ago. And that is similar to a painter’s making the transition from one manner of painting to another’ (MS 183, 141). One might perhaps compare the change in Wittgenstein’s mode of thought to the transformation in the painting of Kandinsky or Van Gogh. The fruits of his early reconsiderations concerning the nature of philosophy were incorporated into The Big Typescript (sections 86–93). But, as noted, he used relatively little of this material in the Investigations. Evidently in 1937 his main concern in this part of the Early Draft was to give a ﬁnal and deﬁnitive diagnosis of what was awry with the methodology and conception of philosophy in his early work, and to ‘turn the examination around’. One root error, he realized in 1937, had been ‘predicat[ing] of the thing what lies in the method [mode, or way] of representing it (Darstellungsweise)’ (PI §104).9 Wittgenstein had in effect chosen a particular way of representing language — in particular propositions (as pictures) and their constituents (as points of contact between language and reality) — and had projected properties of the mode of representation on to the linguistic entities thereby represented. He then thought to ﬁnd simple names and elementary propositions with such-and-such a form in our actual language. And when he could not ﬁnd them in the surface appearances of language, he thought that they must lie beneath the surface. Why must they? Because otherwise the proposition (and the names that compose it) would not be able to do the remarkable things that they evidently do. What are the ‘forms of representation (Darstellungsformen)’ that Wittgenstein has in mind? Whence were they derived? And why did they have such compelling attraction? In 1915 Wittgenstein had written in his notebook, ‘What seems to be given us a priori is the concept: This. — Identical with the concept of the object’ (NB 61).10 The use of the demonstrative, as in ‘By “N” I mean this +’, is one of the most common ways of introducing a name or 9 I shall translate ‘Darstellungsweise’ and ‘Darstellungsform’ as ‘way (or mode) of representation (or representing)’ and ‘form of representation’ respectively, except in those cases in which what is presented is not distinct from the presentation of it, e.g. names or propositions, in which case I shall sometimes speak of modes and forms of presentation. 10 It seems that what he had in mind is that the general form of a name (presumably its simplicity) is given by the demonstrative, and it is identical with the general form of objects, given by the formal concept of an object.

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explaining a name one has used — no matter whether it is a proper name (‘By “Jack” I meant him +’) or the name of a property (‘By “indigo” I meant this +’). It is from this humble prototype that the ‘ideal name’ was derived. ‘The ideal name should function thus’, Wittgenstein wrote in 1937, recollecting what he had thought in his youth (MS 157a, 58v): ‘ “To this name corresponds this”. And the “this” should be simple, completely simple.’ In this way the ‘general form of a name’ was evolved and elevated into an ‘ideal’ that must characterize all real names. The real name, like ‘this’, must be logically unanalysable and be correlated with an object. But that object, like its name, must be simple. What was the appeal of ‘the simple’? What was its prototype? Clearly it was what has captivated philosophers for centuries, including, as Wittgenstein wrote, what is signiﬁed by ‘words like “red”, “dark”, “sweet ”’ (PI §87; BB 31) — i.e. such things as the classical empiricists had subsumed under the misleading heading of ‘simple ideas’. Its appeal was manifold. The only feature Wittgenstein mentioned in his 1937 reﬂections was the desire to represent all change and destruction as forms of decomposition (MS 183, 162f.). This was indeed true of the Cartesian quest for simple natures (hence the Cartesian proof of the immortality of the soul). But it is evident that other considerations were also at work in the Tractatus (where change and destruction get short shrift at best). To the ideal name corresponded the simple object that is beyond existence or inexistence, part of the substance of all possible worlds. The ‘logically proper name’ was meant to eliminate any possibility of referencefailure, to guarantee determinacy of sense, and so to ensure that all surface vagueness would disappear on analysis. It was also the mechanism whereby the proposition, no matter whether it is true or false, could ‘reach right up to reality’ and ensure the pre-established harmony (MS 108 (Vol. IV), 186) between thought and world.11 Parallel to the way of representing names, and the associated idealization, was the corresponding choice of a way of representing (or, indeed, of presenting) propositions, and its associated idealization. How did the Tractatus present propositions? — As pictures or models (‘Bild’ does service for both). What does this amount to? The Tractatus presented the essence of the proposition as being the depiction of a state of affairs. Hence the associated general propositional form: ‘Es verhält sich so-und-so’ (‘Things are thus-and-so’), which (in the case of the elementary proposition) signiﬁes a distribution of ‘objects’ or ‘things’ in a concatenation constituting a state of affairs such that to each name in the proposition there corresponds an object in reality (irrespective of whether the proposition is true or false). Again, we must ask whence this conception. Instead of saying ‘The bottle is blue’, we can say ‘The bottle has the property of being blue’, just as instead of saying ‘The bottle is on the table’, we can say ‘The bottle stands to the table in the relation of being on’. In this 11

For discussion of the ‘pre-established harmony’, see ‘Intentionality’ in Volume 4, pb. edn., Part I.

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perfectly licit rephrasal, it looks as if the essential parts of a sentence form a concatenation of names. For all the words with, as it were, a ‘material meaning’, as Wittgenstein called it, appear to be names distributed in a net of purely logical relations. Moreover, it seems that to each name in the sentence there is a corresponding entity in reality. For ‘the bottle’ signiﬁes this +, ‘the table’ signiﬁes this +, and ‘the relation of being on’ signiﬁes this + (MS 142, §124). So a proposition is akin to a picture or model that depicts a state of affairs — describes how things stand. Indeed, this appeared to be what is essential to any genuine proposition whatsoever — that it be a logical picture. That in turn seemed to give the essence of language, since language just was the totality of propositions that can be generated by the operation N ( joint-negation) on the set of elementary propositions. And that mirrored the essence of the world — the totality of all possibilities. Furthermore, this enabled (or appeared to enable) Wittgenstein to explain all logical relations as consequences of truthfunctional combinations of elementary propositions, and to display all logical truths as limiting cases of truth-functionally combined propositions, i.e. as tautologies.

4. Idealizing the prototype What Wittgenstein had done was to select a prototype which can be found in natural language, and to purify it. He sublimated the humdrum concepts of name and proposition, giving the word ‘name’, for example, a metaphysical use (MS 157b, 14v; see Exg. §116, 2.1(i) and (ii)). And he had generalized a simile, taken a comparison that holds between some types of propositions and depictions of states of affairs for an insight into the essence of the proposition. ‘Tom’, ‘Dick’ and ‘Harry’ are not names of simple objects that lie beyond existence and inexistence. Nor are ‘War and Peace’, ‘The Gardeners’ Arms’ and ‘Eine Kleine Nachtmusik’. But precisely because Wittgenstein was in effect projecting a way of presenting names on to the reality of names, it seemed that there must be such names. So these humdrum names are not the real names. They are adulterated, raw and impure. The real names, of which elementary propositions are constituted, link language to reality. They constitute, must constitute, the foundations of language. Why must they? Because otherwise names could not fulﬁl the functions they must fulﬁl. But, as Wittgenstein now realized, this was a requirement, not a result of experience and investigation. (This realization is, he noted, comparable to Schiller’s response to Goethe’s idea of a primal plant: ‘That is an idea, not an experience’). One cannot, in the present day, say ‘To “Nothung” corresponds this +’ or ‘To “Moses” corresponds this +’. But ‘Nothung’ really is a name, even if the sword has been shattered (or, indeed, is mythical); ‘Moses’ is a name, even if no one was ﬁshed out of the Nile by Pharaoh’s daughter. ‘This +’ (pointing at an ‘indeﬁnable’) is not the general form of a name. Indeed,

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names do not have a general form. They constitute a family, linked by a variety of overlapping resemblances. Corresponding to the ideal name, Wittgenstein had similarly sublimated the concept of a proposition. There is indeed an analogy between certain kinds of proposition and a model (or a history painting) of a state of affairs. But it is only an analogy, and while it holds (like all analogies, up to a point) for certain kinds of proposition, such as ‘This carpet is red’ or ‘The book is to the left of the bottle’, it limps for other kinds of propositions and, as we shall see in a moment, does not hold at all for yet others. But in the Tractatus Wittgenstein had not seen that he was dealing with a simile. For, as he later confessed, because of the grammatical illusion of the unity of concepts, it did not seem like a simile (MS 157b, 6r). For it appeared as if to each name there corresponded a unique object. It seemed as if every concept-word corresponded to one thing, to that which is common to all things falling under it (MS 142, §104). And he had thought that ‘If one proposition is a picture then every proposition must be a picture, since they must all be of the same nature’ (MS 157a, 56r; Z §444). Wittgenstein had in effect transformed an analogy or simile into a way of presenting propositions. The elementary proposition of the Tractatus was presented as a logical picture, i.e. a model of how things stand in reality. The form in which it was presented was as a concatenation of simple names. To each simple name in an elementary proposition there was supposed to correspond a unique and determinate simple object in reality. The elementary proposition was bipolar, dividing logical space precisely into two. It had to be logically independent, so that it could be true or false while everything else remained the same. Its logical independence was a condition for displaying all logical relations as a consequence of truth-functional combinations of propositions by means of the N-operator. But, again, these were requirements driven by a theory, not the result of examining what we ordinarily call ‘propositions’. When we actually look at the phenomena of language, we do not see such propositions. We see a medley of different structures with many different roles. In the Tractatus Wittgenstein had already excluded an important part of what we ordinarily call ‘propositions’, e.g. propositions of ethics, aesthetics and religion (but there seemed very special and deep reasons for doing so), as well as propositions of mathematics. Similarly excluded were such propositions as ‘Red is a colour’ or ‘1 is a number’ (later to be dubbed ‘grammatical propositions’), again, for seemingly deep reasons that chimed with what appeared to be the most important insight in the whole book: namely, the distinction between what can be said and what cannot be said but only shown. But, on reconsideration (in 1937), is it really true that every proposition has, must have, the general form ‘This is how things stand’? Does even as humble a proposition as ‘It is raining’ have this form (MS 142, §127; Z §447)? Does it describe a concatenation of things? Is it, in the requisite sense, a picture or model? Is it, on analysis, a concatenation of names? Indeed, one

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can go further: do propositions of the form ‘If it had been the case that suchand-such, then it would have been the case that so-and-so’ constitute models of how things stand? Do avowals of experience such as ‘I have a pain’ describe concatenations of objects or arrangements of things? (Am I a constituent of the fact that I am in pain?) Are expressions of intention, such as ‘I’m going to go’, pictures of a state of affairs? Accompanying the idealization of the proposition there had been a comparable idealization of the concepts of sense and determinacy of sense. It had seemed that an indeﬁnite sense is no better than no sense at all (PI §99). For how could an indeﬁnite sense be part of the pure crystalline structure of logic? How can an indeﬁnite sense divide logical space precisely into two? And surely experience cannot be indeﬁnite; even if one sees an indeterminate colour (e.g. a ‘dirty’ colour) — what one sees is nevertheless determinate, a quite particular, speciﬁc colour (MS 157a, 64r). Nevertheless, its description may be vague! — Of course, what one says may be vague, but surely what one means is perfectly sharp. After all, ‘if you understand — mean — a sentence, then you must mean something!’ (MS 157b, 4v).12 As Wittgenstein had viewed matters, all surface indeterminacy is, on analysis, determinately indeterminate. For it will be analysable into a disjunction of determinate possibilities (e.g. ‘A is on the table’ is, on analysis, a disjunction: ‘A is there + or A is there + or A is there + or . . .’). This is how it seemed. But it was no more than a commitment to a certain form for presenting vague propositions. And against it Wittgenstein now mustered four objections. First, if one chooses to present vague propositions in the form of disjunctions of determinate possibilities, there can be no guarantee that the constituent conjuncts are determinate (cf. MS 157a, 64r–65r; Z §441). It only appeared to be so on the assumption that to each constituent name in a fully analysed proposition there corresponded one unique thing. Secondly, it is an illusion that what one means by what one says must be determinate. For one does not necessarily mean some thing (some ‘simple object’), even if one always means something. Furthermore, of course, what one means is normally precisely what one says — which may well be vague. Thirdly, one misunderstands the use of ‘quite particular’ or ‘speciﬁc’ here, confusing its intransitive with its transitive use. If every colour one sees, no matter how ‘impure’, is nevertheless ‘quite particular’, this just means that it is what it is and not another thing. By contrast, the transitive use of ‘quite particular’ demands a ‘namely’ rider, in which the determinacy can be cashed by a description (BrB 174 –7). 12

This should be compared with NB 68: ‘It seems clear that what we MEAN must always be “sharp” ’, and NB 70: ‘It is clear that I know what I mean by the vague proposition.’ If someone were to challenge me by arguing that I didn’t know what I meant by a given word in general, I should, with regard to the particular application in question, ‘say: “I know what I mean; I mean just THIS”, pointing to the appropriate complex with my ﬁnger’.

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Fourthly, one has opted for a form in which to present propositions with indeterminate sense. According to this form, nothing, on analysis, counts as indeterminate (since indeterminacy is represented by a disjunction of determinate possibilities). But if nothing counts as indeterminate, then nothing counts as determinate either. So the cost of thus ‘sublimating’ or ‘idealizing’ sense is to render vacuous the claim that all sense on analysis is determinate. And the insistence that sense must be determinate, that an indeterminate sense is no better than none, was tantamount to the imposition of a form of representation for vague propositions, driven by a misconception of the role of logic (see below), which appeared to the young Wittgenstein, no less than to Frege, to impose an irresistible demand for determinacy of sense. In a similar fashion, Wittgenstein had sublimated the concept of a language. A language is not the totality of elementary propositions and the molecular propositions that can be generated from them by the N-operator. For there are no simple names whose meanings are sempiternal simple objects, a fortiori no logically independent elementary propositions composed of simple names. Rather, the propositions of a language form a family of heterogeneous structures united by overlapping similarities, not by common properties (a shared essence, the common propositional form). Speaking a language is not tacitly operating a calculus everywhere governed by rules, but engaging in languagegames loosely, and not everywhere, governed by rules. The boundaries of language are indeterminate, and they include much that is far removed from the sharp structures he had once envisaged. For samples are best considered part of the symbolism of language. Gestures too are not word-language — but was Sraffa’s gesture not a sign, a form of expression (MS 157b, 5v)? What was the logical form of the Neapolitan gesture of contempt? Corresponding to subliming the concepts of name, proposition and language in order to make them conform to the ‘ideal’ which must be in the deep grammar, he had distorted the concepts of object, fact and world. Wittgenstein did not dwell on this in his 1937 reﬂections, having written on the matter in The Big Typescript, and he discussed it in the Investigations only in the context of the criticisms of atomism (with reference to the concept of a simple object). But it is clear that he thought that it was misleading of Frege to call the simultaneous occurrence of a court case and an eclipse of the moon ‘an object’ (PR 137), and that it was a misuse, of which he himself had been guilty, to call a location ‘an object’ (MS 142, §110). So too, he noted that it is a muddle to think that the fact that the glass is to the left of the bottle consists of three objects. When one says that there are three objects on the table, one does not mean the glass, the bottle and their spatial relation. Indeed, it is confused to suppose that facts consist of objects at all (MS 142, §108; MS 127, 75–9; PG 199–201). It is misconceived to claim that the world consists of facts (although it might be said that a true description of (some part of ) the world consists of a statement of facts) or that the world is everything that is the case. As he noted in 1937, he had taken for granted the uniqueness (Einzigheit) or

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determinacy of meaning of the word ‘world’ without having a grasp of the (a?) use of this word (MS 157a, 71r, to MS 157b, 1r).13

5. Misunderstanding the role of the Ideal The Tractatus vision had been sublime. To investigate logic, it seemed, was to investigate the a priori order of things, i.e. of the world. But with the realization that what he had actually done was to project features of a chosen way of representing things on to reality, it became clear that this ‘order of things’ was a myth. He thought that he was investigating the order of the world, whereas, in fact, he was presupposing an order. What he had presupposed was the idea of essence — of the world, of the proposition, etc. (MS 157a, 70r). The words ‘proposition’, ‘world’, etc., and their exceptional importance, lead us to presuppose the existence of transcendent entities with an all-encompassing order (MS 157a, 70v).14 The sublimation of the concept of language to meet the requirements of an ideal had led to the presupposition of an a priori order of the world. What, then, had driven him to the sublimation of language? He had constructed an ideal (the ‘real’ name, the general propositional form, determinacy of sense) out of what he saw in ordinary language. The ideal was part of the form of representation which he had adopted — a form of representation which is not satisﬁed by the surface appearance of the names and propositions of our language. Why did it seem so compelling? It seemed ubiquitous, precisely because it was akin to the spectacles on our nose through which everything is viewed (PI §103). The illusion involved a misunderstanding of the ideal. It seemed as if it must be found in reality, and would be revealed by analysis. This ‘must’ is a mark of the dogmatism that ﬂows from failure to grasp the role of the ideal. Dogmatism here is the thought that things in reality must conform to the mode of representing them, whereas there are two possibilities, neither of which involve any such objective de re necessity. First, it may be fruitful, in certain domains of investigation, to represent one thing in terms of another. So, for example, it may be illuminating to represent the history of cultures in the form of the life of an organism, with a childhood, 13

His wording is rather curious: ‘Ich nahm als gegeben an die Einzigheit der Bedeutung der Wörter “Welt” & “Sprache” ohne dass ich einem Begriff von einem Gebrauch des Wortes “Welt” hatte.’ (Why ‘einem’?) The next remark intimates that the mistake was not to look at examples of the use of the word. 14 ‘In der Meinung die Ordnung der Dinge zu untersuchen, habe ich die // eine // Ordnung der Dinge vorausgesetzt. Vorausgesetzt war die Idee des Wesens (der Welt, des Satzes, u.s.w.). (Der Satz, dieses merkwürdigen Wesens.) Die Wörter “Satz”, “Welt”, u. andere, & ihre ausserordentliche Bedeutung d.h. Wichtigkeit in unserer Sprache) verführen uns zu der Fiktion einer Anwendung dazu, die Existenz transcendenter Wesen anzunehmen mit einer allumfassenden Ordnung.’

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youth, maturity and decline — as Spengler did (cf. MS 157b, 16r–v; see Exg. §131, 2.1(ii)). This may well be a fruitful simile. It is illuminating to look thus upon the rise and fall of Greece or of Rome. But it is mistaken to infer that a culture (e.g. the West) must decline as it ages. It is not as if it could have arteriosclerosis, rheumatoid arthritis or Alzheimer’s disease. For cultures are merely being compared to organisms — and one cannot argue that because a culture has lasted a long time, has already enjoyed a period of greater power and vitality, therefore it is now in old age and must decline and die. In the case of the forms of representation adopted in the Tractatus, it may be illuminating, in certain respects, to compare propositions with models or pictures of how things are, and to present propositions in the form ‘Thus-and-so is how things stand’. But it does not follow that every proposition must be akin to, let alone be, a model or picture of a possible state of affairs, or that every name must have the form of the demonstrative ‘this’ (which form seemed to be the general concept of an object), or that every vague proposition must be determinately indeterminate on analysis. The ideal loses none of its dignity, Wittgenstein points out to Spengler (MS 157b, 16v), by being recognized for what it is: namely, a form of representation. Secondly, there are indeed conventions regarding what is to be called ‘suchand-such’. So, for example, a ﬁgure is called ‘a circle’ only if its circumference is D.π, ‘a triangle’ (in a plane) only if the sum of its interior angles is 180°; and something is to be called ‘red’ only if it is darker than something pink and more similar to something orange than to something yellow.15 But we are prone to project our conventions on to reality, and to interpret what is thus projected as a priori necessities in the world. Then we think that it is of the essence of red to be darker than pink (and that is right, if read rightly), that it is part of the essence of a triangle to have three sides. If A is red and B is pink, we think, then A must be darker than B — which is correct, but misleads us. For we think we have noted a natural necessity. It is, we say, of the nature of red things to be darker than pink. It is an a priori truth about the world, part of the a priori order of the world. But, in fact, all we have done is to note a convention (RFM 65). For the proposition ‘Red is darker than pink’ is no more than a grammatical proposition. It is not a description of an objective necessity, but a rule of grammar. (For examination of Wittgenstein’s later conception of necessity, see Volume 2, ‘Grammar and necessity’.) The idea of ‘the order of things’, of the forms of phenomena, in short of the a priori thus conceived, is a grammatical illusion (MS 157b, 1r–v). The a priori must have its nimbus removed, for it is no more than a form of representation (MS 157b, 3v). That red is darker than pink is a grammatical proposition, a 15

These are indeed conventions, but they are partly constitutive of the concepts concerned, hence interwoven with a mass of further rules for the use of the terms in question to make up a dense network of internal relations. Hence the abandonment of one ramiﬁes through the whole network.

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rule for the use of the words ‘red’, ‘pink’ and ‘darker than’ — a rule that allows us to infer without more ado that if A is red and B is pink, then A is darker than B.16 But when we present a rule for the use of words, a norm of representation, in the guise of a proposition about what is represented, we produce an a priori proposition that appears to be a description of the objective nature or essence of things. For its opposite is excluded — it is impossible, we are inclined to say, that something red be lighter than something pink; and, of course, the opposite is excluded — not by a mythical de re necessity, but because a form of words is excluded (Z §442). Here, unlike the previous case of representing something in the form of another thing, it is not dogmatic to say that if this is such-and-such, it must be thus-and-so. On the contrary, it is perfectly correct. What is mistaken is to think that this ‘must’ does anything more than register a convention, in particular to think that it describes a necessity in nature (‘the logical structure of the world’). We are systematically misled by such grammatical propositions.17 ‘Red is more like orange than like yellow’, we say, and then we investigate this as something given a priori — whereas all that is given is a norm of representation. In an atypical historical remark written in 1937, Wittgenstein observed that it was characteristic of thinkers of the previous cultural period to want to ﬁnd the a priori where there is none, or indeed to have produced the concept of the a priori.18 They would never have done so, Wittgenstein wrote, had they seen things the way we do;19 but then the world would have lost a great and signiﬁcant error. But actually, he concludes, one cannot argue thus, for this concept was grounded in the whole culture (MS 183, 81). Presumably he meant the culture informing eighteenth-century science and the Enlightenment, which presupposed a divine order and inner necessity of things. These misconceptions concerning the a priori order of things in the world were one aspect of misunderstandings concerning the role of the ideal. They 16

Of course, it is no more about the English words than it is about the corresponding words in any other language ( just as the rules of chess are no more about wooden pieces than they are about plastic ones). One might say that it is a rule concerning the concepts of red, pink and darker than — although that too can be misleading. 17 One might say, and Wittgenstein once did (MS 142, p. 86), that the a priori (as exhibited by grammatical propositions) is a form of representation of a form of representation. It is a (highly misleading) way of presenting grammatical rules (these rules themselves determining forms for representing empirical facts): namely, as descriptions. (Similarly, some legal constitutions present norms in the form of descriptions in the habitual present: e.g. ‘The prime minister introduces his cabinet to the President on the third Monday after the election’.) So too, the colour octahedron is an expression of the rules for the use of colour-words (and so a form of representation of colour). The form of presentation of this form of representation is not a sentence of a given form, but a geometrical solid. 18 Initially he wrote ‘or non-concept’ (‘oder Unbegriff ’), but crossed this out. 19 It is unclear whether this is a reference to the way he, Wittgenstein, conceives of the a priori, or to the way the moderns do. If the latter, it is even more unclear whom he has in mind, since there was no general consensus on the concept of the a priori in 1931. So it seems plausible to suppose the former.

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were presuppositions consequent upon misunderstandings about language and logic. The sublimation of names, propositions, determinacy of sense, etc. in the Tractatus involved, as we have seen, projecting a form of representation on to language. Failing to apprehend that this was in effect what he was doing, and failing to ﬁnd such idealized names and propositions instantiated in surface grammar, Wittgenstein had insisted that they must be present in language, if not on the surface, then beneath the surface (to be revealed by future analysis); if not in the conscious mind, then buried beneath the level of consciousness, in the form of tacit conventions of which even the speakers themselves are ignorant (cf. TLP 4.002). However, there is another, equally pernicious misconception of ‘the ideal’. This is the idea that it is a paradigm towards which to strive — as it were, an ideal of perfection. In the context of the reﬂections in 1937, Wittgenstein gives only one example (MS 157a, 66r–v and 68r–v). π is, in the relevant sense, ‘an ideal’; i.e. it is a form of representation. It is a venerable Platonist misconception to suppose that all actual circles are defective in comparison with the ‘Ideal Circle’, which is imagined to subsist sempiternally in a domain of ideal objects. But it is not enough to grasp that the supposition that ‘the ideal’ exists is a Platonist misconception. It can be equally misconceived to suppose that ‘the ideal’ is something towards which we must strive. Then we might say, ‘The circumference of this wheel really is D.π’ (so exactly has it been wrought). But this is misleading. The ideal is the form of expression — not a goal to which all circles approximate, but a form of representation. For a circle is a plane ﬁgure the circumference of which is D.π — these are alternative modes of description. In constructing a circle, we do not strive to construct a circle the circumference of which is D.π — we strive to construct a circle, i.e. a ﬁgure the circumference of which is D.π. The form of representation provides us with an ideal of exactitude.

6. Turning the examination around Wittgenstein’s conclusion — namely, that the examination must be rotated — ﬁrst occurs in this context. The reorientation of our viewpoint is a consequence of realizing that the role of the ideal had been misconstrued. It had seemed as if the ideal was the reﬂection in logic of the ‘a priori order of things’. But the ideal of an objective, a priori order of the world is itself merely a part of the mode of representation (MS 157b, 3r). The very idea that logic must reﬂect the logical form of the world must disappear (MS 157b, 3v). We have to relocate the role of logic. It is not a mirror-image of the world, but a form of representation. In what sense is the viewpoint reoriented? Far from examining the logic of our language in order to discern the a priori order of things in the world, we should examine the logic of our language in order to disclose the illusion of there being any such a priori order of things. Rotating the investigation replaces

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the sublimity of logical investigation with the pathos of the exposure of logicometaphysical illusion (PI §110). The investigation has to be rotated, but about the pivotal point of our real need. What is ‘our real need’? Wittgenstein does not say (the earlier wording (immediately altered) was: ‘our real interests’). It is evidently not a need to ‘understand the basis or essence of everything empirical’, for that was characterized as a misguided urge (PI §89). It is most plausible to suppose that the real need in question is for conceptual clarity, clarity that is attained when one has an overview of the grammatical facts that will dispel the metaphysical illusions that have been under scrutiny. The effect of turning the examination around is to rid us of the preconception of the crystalline purity of logic (PI §108). What was this crystalline purity? If logic is to give us the essence of language (of thought), it must, it seemed, concern itself with pure form — there must be nothing amorphous about it. It must have a transparency, a crystalline clarity that is not to be found in the sciences (MS 157a, 51r). If logic is to present the a priori order of the world, it must surely be utterly simple (MS 142, §95) — ‘simplex sigillum veri’ (TLP 5.4541). For it is prior to all experience, and must run through all experience; it can contain no unclarity or cloudiness, it must be pure crystal — and, indeed, it seemed not an abstraction, of the kind one ﬁnds in the sciences (MS 157b, 10v), but something completely concrete, as it were the hardest of the hard (MS 142, p. 83; cf. TLP 5.5563, cited in PI §97).20 We cannot rid ourselves of this impression, Wittgenstein wrote; it sits like glasses on our nose, and it never occurs to us to take them off (MS 142, §102). But, if we turn our gaze to actual language and carefully observe it, we shall slowly but surely recognize the extraordinary illusion. It will become apparent that the crystalline structure we seemed to see beneath the surface of language was a kind of optical illusion. And only when the causes of this illusion are removed, shall we see language as it really is (MS 142, p. 89). What were the causes of the illusion? One was the failure to realize that what he had been doing was no more than using a simile or analogy, which he had then projected on to the facts (of language). The crystalline purity of logic was not given, it was a requirement (MS 142, §108). The clearer this became, the clearer it also became that this apparently concrete, crystalline structure was an abstraction — a form of representation. The ideal was no more than A similar thought was nicely captured by Lukasiewicz: ‘Whenever I am occupied even with the tiniest logistical problem, e.g. trying to ﬁnd the shortest axiom of the implicational calculus, I have the impression that I am confronted with a mighty construction, of indescribable complexity and immeasurable rigidity. The construction has the effect on me of a concrete tangible object, fashioned from the hardest of materials, a hundred times stronger than concrete and steel. I cannot change anything in it; by intense labour I merely ﬁnd in it ever new details, and attain unshakable and eternal truths. Where and what is this ideal construction? A Catholic philosopher would say: it is in God, it is God’s thought’ (quoted and tr. by P. T. Geach in C. Cooper, P. Geach, T. Potts and R. White, A Wittgenstein Workbook (Blackwell, Oxford, 1970), p. 22).

20

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that; if we pretend otherwise (i.e. if we project these structures on to language and pretend that these strict rules are everywhere), our statements will be empty and senseless, for we are engaged in mere logical trickery (MS 157b, 6r–v). The hidden determinacy of sense was vacuous; the general propositional form was senseless, since nothing was allowed to count as a proposition if it could not be squeezed into this form; the deep, pre-established harmony between language (thought) and reality was empty, since it was tantamount to no more than the intersubstitutability of ‘the proposition that p’ and ‘the proposition that is made true by the fact that p’ (PG 161f.). A further cause of the illusion, as noted, was the misconception that to every name or concept-word there corresponds one thing. The realization that the concepts of a language and a proposition are family-resemblance concepts gives two fatal blows to the conception of the crystalline character of logic. It shows, Wittgenstein averred, that he had not had a general conception of language and proposition. And it dispenses with the aethereal (pneumatic) conception of mental processes (MS 157b, 5v): namely, of understanding as interpreting and of meaning as thinking the sense of a sentence. The idea that the understanding projects simple names on to simple objects in reality by means of acts of meaning can be jettisoned; furthermore (as also became clear) the whole conception of meaning something as a mental act was confused (see Volume 4, ‘The mythology of meaning something’). So, the crystalline clarity becomes no more than a feature of a form of representation, a form of representation by means of the calculus of logic (MS 157b, 5r). What happens to logic? Does not admission of the family character of propositions compromise its rigour? It may seem to do so. For it may appear to call for the disclosure of a logic of vagueness buried beneath the surface grammar of our language. But that is just further illusion, illusion that stems from misunderstanding the role of logic. Logic is not buried beneath the surface of language. Language, from a logical point of view, one might say, is all surface. Logic cannot lose its rigour, and we cannot bargain its rigour out of it (PI §108). We cannot plead for the relaxation of the law of excluded middle, or make arrangements to lift the law of non-contradiction, for the laws of logic deﬁne what is to be counted as a logically valid argument. Logic is a form for the presentation of, and a canon of correctness for, arguments. It is no more affected by recognition of family-resemblance concepts than a system of measurement is affected by the discovery that not all lengths are expressible in complete units. Logic is not what we see beneath the surface of language when we try to penetrate it (PI §90); it is the grid through which we look at arguments when we wish to measure their cogency or to display, with a formal perspicuity, their logical structure. We noted that Wittgenstein remarked that even if the concepts of language were not a family, his new conception would still be different from that of the Tractatus. He did not embroider further. But it seems evident what he meant. For the deepest transformation in his conception of logic, language and indeed

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of philosophy and its method stemmed from the realization that the conception of an a priori order of the world that is to be disclosed by logical investigation into the deep structure of language was an illusion. This insight is independent of the question of the existence of family-resemblance concepts, no matter how important their recognition was for Wittgenstein himself. If anything deserves to be called ‘turning our examination around’, it is the transformation of ‘the a priori’ from being the metaphysical ‘order of things’ into being a mere form of representation, and hence the dissolution of the sublime conception of logical investigation and its replacement by the investigation of the pathos of philosophical illusion. Kant’s Copernican revolution in metaphysics rotated the way of thinking in metaphysics by making the phenomenal world dependent upon our cognitive apparatus, since only thus, he argued, can a priori knowledge of objects be guaranteed.21 Wittgenstein pushed the Copernican revolution much further. He rotated our way of thinking so as to show us that what appeared to be a priori knowledge of the objective order of things was no more than misapprehension of a shadow cast by our forms of representation.

21

Kant, Critique of Pure Reason, B xvii.

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

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Philosophy 1. A revolution in philosophy The great tradition of Western philosophy conceived of philosophy as a cognitive discipline with a subject matter of its own. What that subject matter is was disputed. According to Plato, philosophy is an investigation of eternal truths that yields knowledge of the essences of all things. Aristotle held philosophy to be continuous with the sciences, investigating their distinctive presuppositions and methodological principles. According to Descartes, philosophy seeks to establish the unity of all knowledge and its indubitable foundations in clear and distinct ideas. British empiricists conceived of their subject as an investigation of the nature and limits of human understanding. With Kant’s Copernican revolution there occurred a paradigm shift: philosophy should concern itself not with knowledge of objects, but with the mode of our knowledge of objects in so far as it is possible a priori. He held that philosophy results in knowledge of synthetic a priori propositions that are pre-conditions of experience. Within this tradition, there was one unshakable conviction: namely, that philosophy is a cognitive discipline, that there are philosophical propositions expressing philosophical knowledge. Wittgenstein, in his ﬁrst philosophy, pursued the goals of the ‘Great Tradition’, in particular the metaphysical goal of disclosing the a priori order of the world. Philosophy, he had declared at the very beginning of his investigations, consists of logic and metaphysics, the former its basis (NB 106). For logic seemed to be ‘the great mirror’ of the essence of the world (NB 39), and logical investigation seemed to ‘explore the essence of all things’ (PI §89). As his work progressed, he distinguished between what can be said by the use of a symbolism and what is shown but cannot be said by it (‘Notes Dictated to G. E. Moore in Norway, April 1914’, NB 108–19). Just as Kant drew the boundaries of knowledge in order to make room for faith, so Wittgenstein drew the boundaries of sense in order to make room for ineffable metaphysics. The essence of the world is shown, but cannot be said, by language. It is shown by fully analysed bipolar propositions and by the vacuous tautologies of logic. But in thus drawing the bounds of sense, he no more meant to throw away metaphysical insight than Kant, in drawing the boundaries of knowledge, meant to throw away belief in God and in the immortality of the soul.

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As a result, there is a gulf dividing the Tractatus practice of philosophy from the programme for future philosophy which it proposes. The sentences of the book range from discussions of the foundations of logic to the essence of the world (NB 79) — but these sentences are ﬁnally recognized to be attempts to say what can only be shown. They transgress the bounds of sense, and so are nonsensical. But the attentive reader who understands the author will attain a correct logical point of view and see the world aright. For, as Wittgenstein noted in the Preface, ‘the truth of the thoughts that are here set forth’ seemed to him to be ‘unassailable and deﬁnitive’ — even if, strictly speaking, ineffable.1 Since ‘on all essential points’ he had found ‘the ﬁnal solution to the problems’ (‘Preface’, p. 5),2 the task of future philosophy is quite different from the task that was deﬁnitively completed by the Tractatus. Constructively, it is an activity of logical clariﬁcation of thoughts by analysis, which will lay bare their logical forms and make evident their determinate senses, both of which are obscured by surface grammar (TLP 4.112).3 Destructively, its task is to demonstrate to any would-be metaphysician that he has transgressed the bounds of sense (e.g. misused formal concept-words) and has failed to give a meaning to certain signs in his sentences (i.e. to the formal concept-words thus employed (TLP 6.53)). Precisely because the logical syntax of language was supposed to reﬂect the essence of the world, and because logical investigation of language was supposed to be the means for attaining insight into the ultimate nature of all things, the Tractatus initiated what later became known as ‘the linguistic turn’ of twentiethcentury analytic philosophy. This was manifest in the claim that ‘All philosophy is a critique of language’ (TLP 4.0031). The aim of the Tractatus was to set the limits of thought. But they can be set only by describing the limits of the expression of thoughts, i.e. the limits of language — the demarcation of sense from nonsense (Preface, p. 3). This put the investigation of language on to centre-stage. Further, the key to Wittgenstein’s endeavours lay in his clariﬁcation of the essence of the proposition, i.e. of the sentence in its projective relation to the world. This was achieved by elucidating the general propositional form, i.e. by giving ‘a description of the propositions of any signlanguage whatsoever in such a way that every possible sense can be expressed 1

That there is tension between the claim that the thoughts set forth are true and the subsequent claim that the sentences of the book must be recognized as nonsensical, i.e. as attempts to say what cannot be said but can only be shown, is undeniable. But then, as Wittgenstein said later, the book is akin to a clock that was meant to tell the time, but actually does not work. 2 He repeated this claim in his letters to Russell: ‘I think I have solved our problems ﬁnally’ (CL 60); three days later he wrote: ‘I believe I’ve solved our problems ﬁnally. This may sound arrogant but I can’t help believing it’ (CL 61). In a letter to Keynes he wrote: ‘Have you done any more work on probability? My MS contains a few lines about it which, I believe, solve the essential question’ (CL 63). 3 First steps towards clarifying the logical form of propositions about perceptual qualities in the visual ﬁeld were taken in ‘Some Remarks on Logical Form’ in 1929, at which point the whole enterprise began to unravel over determinate exclusion (colour incompatibility).

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by a symbol satisfying the description and every symbol satisfying the description can express a sense, provided that the meanings of names are suitably chosen’ (TLP 4.5).4 With the progressive disintegration of the Tractatus philosophy between 1929 and 1931, a new vision and a new method emerged. Wittgenstein had viewed the Tractatus as the radical culmination of the philosophical tradition, pursuing insights into the essence of the world by logical investigation. With the demise of that conception and the emergence of a new method, Wittgenstein selfconsciously engendered a revolution in philosophy. On the one hand, he considered himself to be the destroyer of the great tradition of Western philosophy, to be remembered perhaps only like the man who destroyed the library at Alexandria (MS 183, 63). For the systematic destruction of the deepest ideas that informed the Tractatus evidently seemed to him also to be the destruction of the deepest presuppositions of traditional philosophy. On the other hand, he thought of himself as transforming philosophy into something new. In his 1930 lectures, he said that ‘the nimbus of philosophy has been lost’. It can no longer be thought to be the Queen of the Sciences. It has lost its sublimity. It cannot aspire to investigate the objective (language-independent) essence of all things, since there is no such thing. What he is now doing, he asserted, is a new subject, and not merely a stage in a continuous development. It is one of the heirs of what used to be called ‘philosophy’. There is now a kink in the development of human thought, comparable to that which occurred when Galileo invented dynamics. For a new method has been discovered. Now, for the ﬁrst time, it is possible to have skilful philosophers (M 113; LWL 21; BB 28). The transformation of the subject that Wittgenstein had in mind was the abandonment of all that had seemed sublime about the aspirations of philosophy from Plato until Frege and Russell.5 Those aspirations rested on a multitude of illusions, at the heart of which was the assumption that philosophy 4

Frege is sometimes credited with originating the linguistic turn. He would, perhaps, have been surprised at this, for he wrote to Husserl in 1906: ‘It cannot be the task of logic to investigate language and determine what is contained in a linguistic expression. Someone who wants to learn logic from language is like an adult who wants to learn how to think from a child. When men created language, they were at a stage of childish pictorial thinking. Languages are not made to match logic’s ruler’ (PMW 67f.). For more detailed discussion of the ‘linguistic turn’, see the epilogue to this Commentary, Wittgenstein’s Place in Twentieth-Century Analytic Philosophy (Blackwell, Oxford, 1996), pp. 36–8. The ‘turn’ was not completed, one might say, until the metaphysical baggage (including the metaphysics of symbolism) was jettisoned in the 1930s, both by Wittgenstein and by the Vienna Circle. For discussion of Frege’s equivocal attitude to natural language, see G. P. Baker and P. M. S. Hacker, Frege: Logical Excavations (Blackwell, Oxford, 1984), ch. 3. 5 According to Frege, whose interests were largely conﬁned to logic and philosophy of mathematics, logical investigation studies the laws of truth that govern the relations between all thoughts — ‘the boundary stones set in an eternal foundation which our thought can overﬂow, but never displace’ (BLA i p. xvi). According to Russell, logical investigation studies the most general facts in the universe and catalogues their logical forms.

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was a cognitive discipline with a genuine subject matter of its own. Our whole way of thinking must be rotated (PI §108), so that we abandon the illusion that logical investigation can yield insight into the a priori order of the world and the necessary depth structure of all thought and language (see ‘Turning the examination around: the recantation of a metaphysician’). We must reject the old idea of the great Western philosophers that there are two kinds of problems in the ﬁeld of knowledge: the essential ones, which it is the task of philosophy to investigate, and the inessential, quasi-accidental ones, with which the empirical sciences deal. There are no great essential problems, only great and compelling illusions of such problems (BT 407). The task of philosophy is to investigate the grammar of our language in order to clear the ground of language of such houses of cards (PI §118). There are no philosophical propositions, effable or ineffable, and there is no philosophical knowledge, sayable or showable. Philosophy is a contribution to human understanding, not to human knowledge. Philosophical problems are an awareness (not typically a self-conscious one) of a disorder in our concepts. They are to be solved by ordering those concepts (BT 421). The problems of philosophy are posed by questions that can be answered neither by the natural sciences, since they are not empirical questions at all, nor by the mathematical sciences, since they are not questions demanding proofs of new theorems. They are not practical questions; puzzlement about how it is possible to measure time is not solved by showing one how a clock works (BB 30f.) Rather, they are questions that manifest (often unselfconsciously) a conceptual unclarity. Sometimes they are questions in search of a sense, rather than of an answer. Sometimes they are questions that are to be resolved not by answers, but by further questions that will dissolve them. For when ‘a confusion is expressed in the form of a question that does not acknowledge the confusion’, then ‘what releases the questioner from his problem is a particular alteration of his method of expression’ (PG 193). More generally, they are resolved by attaining an overview of a segment of the grammar of our language that will enable one to recognize where one went astray. The problems of philosophy are conceptual, not factual, ones (Z §458), and they are to be resolved by a grammatical investigation (AWL 97). Their product is not insight into or knowledge of the essence of the world or the workings of the human understanding or the hidden essence of language, but the dissolution of the problems and an overview of (some part of ) the web of language. The transformation is profound, and one might well wonder why what Wittgenstein was now doing should be conceived of as an ‘heir’ to what used to be called ‘philosophy’. He gave various reasons. It resembles traditional philosophy in its generality, in its being fundamental to ordinary life and to the sciences, and in its being independent of any special results of science (M 113). There is an analogy between what he does and what Plato was doing. It takes the place of what Plato was doing, in the sense in which the algebraic solution to the trisection problem took the place of (the quest for) a geometrical

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one (see Exg. §334, §463). The new activity resolves or dissolves the problems that the old one tried to answer (cf. AWL 27f.). For the same problems that occupied the Greeks in an important sense unavoidably still occupy us (and there are deep reasons for this: namely, the persistence of similarly misleading grammatical forms (BT 424)). Is Wittgenstein’s new philosophy the only heir to what was traditionally called ‘philosophy’? Clearly not. For among the things investigated by what used to be called ‘philosophy’ were the natural sciences (long denominated ‘natural philosophy’), empirical psychology (which attained independence only at the end of the nineteenth and beginning of the twentieth centuries), and mathematical logic (now being assimilated into mathematics). But are there other philosophical heirs? Wittgenstein gave no sign of thinking that there were other, intellectually respectable ways of handling the questions he dealt with than the methods he now advocated. What, then, was ‘the new method’ which he declared ‘had been found’? He characterized it in late 1929 as being essentially the transition from the quest for truth to the quest for sense (‘Diese Methode ist in Wesentlichen der Übergang von der Frage nach der Wahrheit zur Frage nach dem Sinn’). The observation is striking, because one might have thought that the Tractatus had already made this ‘linguistic turn’. But it seems improbable that he would write this in 1929 had he been referring to methods that already characterized his work ﬁfteen years earlier. It is more likely that by ‘the transition to the question of sense’ he meant the description of the grammar of our language for the purpose of dissolving philosophical problems, and the rejection of aspirations to investigate truths about the essence of the world by investigations into a hidden depth grammar (as envisaged in the Tractatus). Be that as it may, it is evident from Moore’s notes that what Wittgenstein said in his classes about the new method refers to such grammatical descriptions (M 113f.). In philosophy, he now declared, everything that isn’t gas is grammar (LWL 112). Logical investigation had seemed to promise the map of Treasure Island, and the promised treasure was insight into the ultimate nature of all things. We still need a map, but the map is the treasure — for it will enable us to ﬁnd our way around the labyrinth of language. Hence the rotation of our examination or way of thinking that Wittgenstein wrote of in 1937 is a further aspect of this same transformation in his conception of the nature, goals and methods of philosophy that dawned on him in 1929/30. It was, as noted (see ‘Turning the examination around: the recantation of a metaphysician’, p. 269), no less than another Copernican revolution in philosophy. Why did the new method imply that there could now be skilful philosophers? Why could there not have been skilful philosophers in the past? Perhaps because as long as philosophers laboured under the illusion that their quest was for the essence of the world, the foundations of knowledge, and the ultimate principles of human understanding, there could be no skills in producing what was sought (which is not to say that what was produced was not often of great

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interest). Descartes was a great philosopher, but there can be no skilful neoCartesians who carry on the work of uncovering the indubitable foundations of all human knowledge. Hume was a great philosopher, but there can be no skilful neo-Humeans, who carry on the work of investigating the patterns of association of ideas that determine the scope and limits of human knowledge. In the past there could be great philosophers, gripped by a metaphysical vision. But with Wittgenstein’s new conception of what philosophy now is, and of what it can and cannot do, there is a new method — indeed, a multiplicity of methods. The philosophically relevant description of the grammar of words, the disclosing of misleading analogies and disanalogies between uses of words, the arrangement of the grammatical data to exhibit the precise character of the philosophical illusion that grips us, the noting of the circumstances of use, the detection of misleading pictures in language, etc., etc. — all these are matters of skill. The appropriate exercise of such skills produces results — clariﬁcations, apprehension of conceptual afﬁnities and differences, ordering of concepts, that are permanent achievements, and can ‘be put in the archives’ (BB 44). A corollary of this is that philosophy need no longer torment itself with questions that call itself in question (PI §133). The great philosophical systems of the past rested on presuppositions. Plato presupposed a realm of abstract entities by reference to which he thought to explain the character of items in the phenomenal world. Descartes presupposed that there are indubitable propositions that constituted the foundations of empirical knowledge. Hume presupposed that the medium of thought is the ideas with which the mind is furnished by experience. Kant presupposed that there are synthetic a priori propositions that describe how things necessarily are in the world. The Tractatus presupposed that names have meanings, i.e. simple objects constituting the substance of the world, and that elementary propositions have sense (TLP 6.124), i.e. are essentially pictures of possible states of affairs. In all such cases, if the presuppositions are challenged, the whole philosophical ediﬁce is challenged. And if the challenge is warranted, the ediﬁce collapses. The challenges were warranted, and the ediﬁces did collapse. Wittgenstein, by contrast, now offers a conception of philosophy which does not rest on any such questionable presupposition. Now one can ‘stop doing philosophy whenever one wants to’, secure in the knowledge that philosophy itself, thus conceived, cannot be called into question. Problems are solved, difﬁculties eliminated — not one great problem6 (PI §133). Doing philosophy is comparable to the ordering of books in a library: achievement consists in the realization that these books belong together, and those books should be kept apart — even if the ﬁnal placing on a given shelf of the books thus conjoined or sundered may be altered (BB 44f.). 6

So not, for example, ‘How is synthetic a priori knowledge possible?’ or ‘What are the indubitable foundations of knowledge?’ or ‘What is the essence of the proposition?’ (The Tractatus had observed that ‘To give the essence of the proposition means to give the essence of all description and thus the essence of the world’ (TLP 5.4711)).

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2. The sources of philosophical problems Philosophy, Wittgenstein said, is nothing but philosophical problems (PG 193). Philosophical problems are best characterized by examples, for they form a family that is not fruitfully circumscribed by an analytic deﬁnition. Of course, one can say that they are conceptual, a priori problems. That serves to distinguish them from scientiﬁc problems, and to differentiate philosophy from natural science. But it does not demarcate them from things that have nothing to do with philosophy, such as mathematics. (Mathematics, unlike philosophy, is concept-formation.) Philosophical problems and difﬁculties rest on misunderstandings (MS 109 (Vol. V), 298) — conceptual misunderstandings. They do not require new discoveries, but patient unravelling. (The door does open — one need only understand the lock and turn it in the right way.) It is not the task of philosophy to set up a ‘system of the world’, but only to intervene where conceptual difﬁculties and confusions emerge (VoW 125). The character of the problems that Wittgenstein called ‘philosophical’ can be illuminated by examining the sources to which he ascribed them. One great source of problems is the misleading features of the grammar of our language. These are varied. Expressions with very different uses may look alike, while expressions with similar uses may look different. ‘To have a house’ looks like ‘to have a mind’, but the former signiﬁes a form of ownership, whereas the latter does not, and a house is a kind of substance, whereas a mind is not. ‘Jack is taller than Jill’ has the same grammatical form as ‘3 is greater than 2’, but the former is a description of how things are, and the latter is an expression of a rule. ‘Bachelors are unmarried’ seems akin to ‘bachelors are unhappy’, but it is not. Conversely, ‘Red is a colour’ appears quite different from ‘whatever can be said to be red, can also be said to be coloured’, but actually fulﬁls much the same role. ‘It is impossible for a thing to be red all over and green all over’ looks unlike ‘there is no such thing as being red and green all over’ and also unlike ‘the form of words “simultaneously red all over and green all over” has no use’, but the three sentences do not typically differ in their function. Because there are such superﬁcial similarities of grammatical form concealing differences of use and of implication, and differences of grammatical form concealing similarities, we jump to the wrong conclusions. We think that the mind is a substance, that arithmetical propositions are descriptions of relations between numbers, that norms of representation are descriptions of necessities in the world. We ask inappropriate, misconceived questions. Because ‘to understand’ appears akin to a verb of action, we ask, ‘How does one understand a sentence one has never heard before? — as if understanding were an act or activity one performs, of which it makes sense to ask ‘How do you do it?’. For it then seems as if understanding were a hidden inner mechanism, and as if we were asking how the mechanism works. Whereas to understand an utterance is not to do something, but to be able to do various things (e.g. to respond

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appropriately to what was said, to act on the utterance or its content, to explain what was said) — and while one can ask how one came to be able to do something, one cannot ask how one does being able to do something. ‘Having a penny’ looks like ‘having a pain’ or ‘having a thought’, and philosophers, such as Hume and James, have wondered whether there can be ownerless pains or thoughts as there can be ownerless pennies. We speak of painted images, which anyone can see in a picture gallery, and also of visual images; and we are inclined to think that only the ‘owner’ of the visual image, the person who has it, can see it. And some scientists conduct experiments to ﬁnd out whether there are visual images which their owner fails to see (vide neuropsychological research on so-called blindsight). But to have a visual image is not to own anything — let alone a ‘private’ picture; to ‘see’ a visual image just is to have one; and there is no such thing as having a visual image that one does not have (‘see’) any more than there is such a thing as having a pain one does not feel. A related source of confusion derives from our failure to notice that although a fragment of one language-game may be analogous to that of another, nevertheless the two are not homologous. So we mistakenly project features of one on to the other, and draw inferences and raise questions that ﬁt one but not the other. We say, for example, that it is certain that it will rain today, that it is certain that 25 × 25 = 625, that it is certain that the world has existed for a long time, and that it is certain that I have a toothache. We take it for granted that these certainties are, if distinct at all, distinct only in degree (proven mathematical truths, we think, have the highest degree of certainty). But that is quite wrong. These are different kinds of certainty, with different kinds of grounds (or none at all) and different kinds of consequences. Similarly, we talk of believing that it will rain tomorrow, that ℵ1 is greater than ℵ0, that promises ought to be kept, or that pigs can’t ﬂy. Believing, in each case, is, we think, the same ‘propositional attitude’. It just happens to be directed at different ‘objects’. We fail to see that to believe a mathematical proposition is radically unlike believing an empirical one (it is more like believing that the chess king is the piece that is checked).7 We know what it is to believe that it will rain tomorrow and also what it is to believe that it will not. What is it to believe that a triangle has ﬁve sides, or that 1086 < 3 or that 12 × 12 = 5? We talk of its being true that horses are larger than donkeys, that red is darker than pink, that 25 is greater than 20, that either p or not-p. But we do not pause to reﬂect on the differences in what it means to say that it is true that. . . . For although ‘true’ is unequivocal, proposition is a family-resemblance concept, and there are prodigious differences between propositions of different kinds, which are reﬂected in differences in what it means to say that such-and-such is true (see ‘Truth and the general propositional form’, sect. 5). The truth 7

For discussion of the epistemology of the a priori, see Volume 2, ‘Grammar and necessity’, sect. 4.

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of a mathematical proposition is no more akin to the truth of an empirical proposition than a chess queen is akin to a queen. Embedded in the grammar of our languages are innumerable ‘pictures’, as it were, emblematic representations,8 which are endlessly misleading. It was noted above that the picture of ownership or possession is dragged along with the use of the auxiliary verb ‘to have’. We speak of having a pin and also of having a pain, a body and a mind — so we think we own our sensations, own our body (and passionate argument in moral and political philosophy (e.g. concerning the right to abortion) turns on this confusion) and own our own mind. Here we are taken in by a picture and fail to see the grammatical differences, e.g. that if I sell the pin I have, it is no longer my pin, but there is no such thing as selling my pain (and that is neither because this is a case of logically inalienable ownership, nor because there would be no buyers). Although I can sell my body, it does not cease to be my body when I do so. For ‘to sell my body’ means ‘to sell sexual services’ — what I then lack is a choice, not a body. And if I lose my mind, it is no use advertising to see if anyone has found it. We ﬁnd ourselves mesmerized by wrong and misleading pictures. Suppose someone decided to introduce talk of ‘unconscious toothache’ to signify a rotten tooth that does not hurt. This would be misleading, for it may appear as if a discovery had been made (just as Freud thought that he had discovered something new in his talk of ‘unconscious feelings or motives’, whereas he had introduced a new notation, a new and sometimes illuminating way of talking about familiar phenomena). Then one may wonder how on earth there can be unconscious toothache. A scientist may urge that there are lots of things one does not know, and insist that it has now been discovered that one can have toothache and not know it, that this is a scientiﬁc fact (BB 22f.). Another example Wittgenstein discusses is the picture that comes naturally to us in reﬂection on contradictions. One thinks of a contradiction as ‘jamming’ — things cannot move, as it were (LFM 190). But this picture is confused, for then we think that what are jamming are the meanings of the words — as if they were solids that could either mesh with adjacent meanings or jam (see discussion of ‘meaning-bodies’ in Exg. §138). Similar confusions are engendered by misapplying perfectly correct pictures (see Exg. §§422–6). Very often the pictures we use are innocuous, e.g. as when we say ‘I should like to know what is going on in his head’, but in philosophy (and psychology) we misapply the picture. Wittgenstein illustrated how it can come about that we get hold of the wrong end of the stick. Suppose we stretched a cord around the circumference of the earth, and then added one yard to it. Assuming the cord was kept taut, circular and equidistant from the surface of the earth, how far from the surface would it be? We are 8

Bentham noticed this point too, referring to verbal pictures, such as ‘being bound by an obligation’, as ‘archetypes’, and to the activity of explicating them and rendering them philosophically harmless as ‘archetypation’.

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unreﬂectively inclined to think that it would be imperceptibly close to the surface. Actually, it would be nearly six inches from the face of the earth. Here we have a correct picture: namely, that a yard added to the string is a minute fraction of the length. From this we mistakenly conclude that adding a yard to the circumference will add a minute length to the radius (rather than that the increase of the length of the radius will be a minute fraction of the length of the radius). Here we misapply a correct picture.9 Similarly, one picture we have of thinking is of Le Penseur talking to himself (RPP I, §549). But we are prone to misapply this picture, to suppose that thinking is talking to oneself. And then we suppose that the thoughtful tennis-player talks to himself (very quickly) while he is playing, and that the thoughtful conversationalist talks to himself while he is talking thoughtfully aloud! And we are, perhaps, stopped in our tracks only by the reminder that one can talk to oneself thoughtfully or thoughtlessly; and if the former, does one say everything to oneself twice? Here, we don’t know our way around in the use of our picture, and that in turn just means that we do not know our way around our use of the word ‘to think’ (ibid.). A different source of problems is an obsession with a certain language form (AWL 98f.). One might say that Wittgenstein had been obsessed in the Tractatus with one variant of the declarative form of sentences, viz. ‘such-and-such is thus-and-so’ — which he then proceeded to project upon the imagined depth grammar of every possible sentence in every possible language. Rather differently, he said of himself, when he was struggling to free himself of the misconceptions about intentionality that were built into the picture theory, that he was entrapped by the word ‘what’, obsessed with the phrase ‘what one believes (expects, fears, etc.)’. For surely what one believes when one believes truly must be what is the case when one’s belief is true; but how can that be, given that what one believes may not be the case. Moreover, if it is not the case, then what one believes does not exist. Does one then believe nothing? No, what one believes is exactly the same, no matter whether one believes truly or falsely — but how can that be? These different sources of confusion take us in. We pursue chimeras, and erect castles in the air. Although we are masters of our native tongue, we do not know our way around the grammar of our language. Language contains the same traps for everyone; the immense network of well-kept // passable // false paths. And so we see one person after another walking the same paths and we know already where he will make a turn, where he will keep on straight ahead without noticing the turn, etc., etc. Therefore, wherever false paths branch off, I should put up signs which help one get by the dangerous places. (BT 423) 9

N. Malcolm, Ludwig Wittgenstein: A Memoir, 2nd edn (Oxford University Press, Oxford, 1984), p. 46.

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However, it would be quite mistaken to suggest that Wittgenstein held that all philosophical problems arise from the grammar of our languages. There are other sources of philosophical confusion, which lie in our culture. One such source is to be found in the success of scientiﬁc theory and explanation that has marked Western civilization over the last four centuries. ‘Philosophers constantly see the method of science before their eyes, and are irresistibly tempted to ask and answer questions in the way science does. This tendency is the real source of metaphysics, and leads the philosopher into complete darkness’ (BB 18). The deceptive model of science inclines philosophers to think that what they are in search of is (i) a theory; (ii) an explanation on the model of science; (iii) the reduction of phenomena of one kind to phenomena of another, on the model of scientiﬁc reduction of explanations of natural phenomena to the smallest number of primitive laws, and also the reduction of expressions of one kind to expressions of another kind; (iv) analysis of concepts on the model of scientiﬁc analysis of phenomena. Reductionism in philosophy is perhaps less popular among philosophers than it was when Wittgenstein wrote. But the scientiﬁc model of explanation, and indeed the idea that what philosophers should be doing is inventing new theories to explain phenomena, is as powerful as ever. For the perennial temptations of metaphysics incline philosophers to try to explain what appear to be necessities in nature on the model of scientiﬁc inferences to the best explanation. Against this, as we shall see in section 5 below, Wittgenstein argued that ‘it can never be our job to reduce anything to anything’ (‘Everything is what it is and not another thing’), and that it is not the task of philosophy to explain anything in the sense in which the natural sciences explain things. It is at best misleading to say that we want an analysis of our concepts, since ‘analysis’ in science betokens new discoveries: namely, information about the hidden constitution of things. Moore’s idea that we must wait upon analysis to tell us what we mean by our propositions and whether we mean anything by them is ‘a hellish idea’ (WWK 130), as is Frege’s assumption that no one knew what numbers are (what number-words mean) until he came up with a recherché deﬁnition (that very few users of number-words could understand). In philosophy, unlike science, we already have all the information we need (M 114); what we lack is an overview of the grammar of problematic expressions, and the skills to order the grammatical data so as to dispel illusion. It is not only the model of scientiﬁc theorizing that distorts philosophical reﬂection, but also actual advances in science. The power of a successful scientiﬁc theory may induce philosophers to try to explain conceptually bafﬂing things on analogy with that speciﬁc model (as Hume modelled his investigations into human understanding on Newton’s physics). Sometimes, Wittgenstein pointed out, a scientiﬁc language ‘produces an obsession’ with a particular pattern of explanation — as happened with the discovery of dynamics (AWL 98). Advances in physics generate fresh confusions in philosophical

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reﬂection (some philosophers have thought to ‘save’ human freedom by reference to Heisenberg’s Uncertainty Principle). Discoveries in chemistry, such as the Periodic Table, induce the thought that nature classiﬁes things of her own accord, and that it is for us to ensure that our concepts mirror the divisions in nature.10 Similar sources of confusion arise in the a priori sciences. The model of geometry, the greatest systematic achievement of Greek thought, fascinated Plato and was a primary source of a fundamental distortion of the concept of knowledge, which then dogged European philosophy for more than 2,000 years. Frege’s and Russell and Whitehead’s invention of the predicate calculus mesmerized twentieth-century philosophers, producing the misconceptions that such calculi are logically ideal languages, or are the underlying depth grammar of all possible languages, or reﬂect the logical structure of the world. Mathematical logic, Wittgenstein declared, has completely distorted the thinking of philosophers (RFM 300). Other sources of conceptual confusion, of our inexhaustible capacity to tie knots in our understanding, lie in our own nature. (i) We have a craving for generality, which is a spur to scientiﬁc ingenuity in devising ever more powerful and general theories. Naturally enough, we follow this urge to generalize when struggling with conceptual problems, and all too commonly demand generality where only particularity is meet. (ii) We have a craving for unity, which informs our scientiﬁc endeavours, in which we seek to subsume the greatest multiplicity of phenomena under a single all-encompassing law. And we follow this disposition of reason in our philosophical investigations too. So we are prone to assume that everything that falls under a concept-word does so because of possession of a common characteristic or characteristics, and shun the idea that the extension of a concept is often a family, united only by overlapping similarities. (iii) Ever since Plato, who was inﬂuenced by the methods of Greek geometry, philosophers have craved deﬁnitions, which will exhibit the essential nature of what falls under them. Like Plato, they are inclined to think that the solution to philosophical problems is to be found by searching for a deﬁnition of the term that is causing trouble. Wittgenstein thought this to be misguided. Deﬁnitions do not disclose essences, they determine them. They give rules for the use of words, not insights into the language-independent essence of things. In the case of some problematic expressions, there is no strict deﬁnition, and it is doubtful whether one can be devised. But more importantly, the source

10 Wittgenstein did not advert to the deleterious impact of technological advance on philosophical reﬂection. The invention of clockwork had a powerful impact on the thought that organisms are mere machines, and on the conception of determinism that dominated eighteenth-century thought. More recently, the invention of the computer has wrought havoc with our thought about the brain and mind — no longer a central telephone exchange and its operator, the brain is now a computer, and the mind its software.

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of the trouble is very often such that even if we were to come up with an adequate deﬁnition, it would not resolve the difﬁculty. Augustine’s troubles with time would not be eased by giving a deﬁnition, and puzzlement over the nature of number is not (pace Frege) solved by coming up with a recherché deﬁnition — for it was not lack of a deﬁnition that caused the conceptual puzzlement in the ﬁrst place (BB 27). Nor will the bafﬂement disappear by declaring the problematic notion to be ‘simple and indeﬁnable’ — as Moore proposed with respect to goodness (PI §182). (iv) The urge to explain phenomena, to answer the question ‘Why?’, is the root of the scientiﬁc endeavour to render nature intelligible to us. We transfer the craving for explanation to philosophy, and think to answer philosophical questions on the model of explanations in the natural sciences (and sometimes on the model of mathematics). We are then oblivious to the fact that there are problems, both within philosophy and in other domains (e.g. anthropology, aesthetics), that are resolved by an arrangement of the data which will render them perspicuous and make it possible to apprehend formal relations between them (see ‘Surveyability and surveyable representations’). (v) We have a metaphysical urge to seek necessities where there are none. We project features of our forms of representation on to reality, think we discern the necessary structure of language or of the world, and then try to explain these illusory necessities. ‘The greatest danger in philosophy comes from the metaphysical tendency that completely distorts grammar’ (MS 116 (Vol. XII), 256). (vi) We have a myth-building tendency, a proneness to erect mythologies instead of simply describing phenomena. This is obvious in our disposition to personify forces of nature, and the mythologies that mankind has woven around such personiﬁcations. What is less obvious is the fact that there is an entire mythology embedded in our language (BT 434) — a mythology of the mind as a space, of time as a river, of space as a receptacle, of introspection as a form of perception, and so forth. In philosophy we are all too prone to be taken in by such turns of phrase. Furthermore, we create further mythologies in our philosophy. ‘In philosophy we are always in danger of giving a mythology of the symbolism, or of psychology: instead of simply saying what everyone knows and must admit’ (PR 65). Wittgenstein himself had succumbed to this tendency in the Tractatus: the ‘real (logically proper) name’, the ‘real elementary proposition’ (to be found perhaps only in the mysterious workings of the mind), and the general propositional form were mythologies of symbolism (like the depth grammar of late twentieth-century linguistic theory). The idea of acts of meaning and interpreting as constituting the method of projection of signs on to states of affairs and their constituents was a correlative mythology of psychology (like the computational mechanisms attributed to the mind or ‘mind/brain’ by modern cognitive science and linguistic theory). Good philosophy works against this myth-building tendency of our understanding (MS 158, 28r).

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3. The goals of philosophy: conceptual geography and intellectual therapy Since philosophy is not a cognitive discipline, its goal is not to discover new truths or to accumulate knowledge. Wittgenstein characterizes the aims of philosophy both positively and negatively. The positive aims are subservient to the negative ones. Positively, philosophy aims to attain an overview of a conceptual ﬁeld, to arrange grammatical data so that the manifold relationships become perspicuous. Negatively, philosophy aims to disentangle conceptual confusions, to destroy metaphysical illusions, to undermine mythologies of symbolism and of psychology. It is, as it were, a cure for certain kinds of diseases of the understanding. Wittgenstein compares philosophy both to medical therapy and to psychoanalysis. Wittgenstein’s conception of an overview is examined in ‘Surveyability and surveyable representations’. Here I merely note that to attain an overview, in philosophy, is to grasp the salient grammatical features of the problematic term and apprehend the relationships between its use and that of other expressions with which it might wrongly be conﬂated or from which it might wrongly be differentiated. Giving a synopsis of the use of an expression, describing its salient grammatical features, and rendering a surveyable account of the relevant conceptual relationships is a positive achievement. One who has an overview knows his way around in the grammar of the problematic expression and is in a position to clear up associated philosophical confusions. The point of striving for an overview is to clear up philosophical difﬁculties, to make the troubles disappear. Where there are none (say in culinary discourse), there is no point in striving for an overview of concepts. For where there are no such troubles, there is nothing to make disappear. The ﬁeld of philosophy is limited by the ﬁeld of our philosophical troubles (MS 150, 32). It was natural, against this background topographical metaphor, that Wittgenstein should have invoked the further metaphor of logical or conceptual geography, a conceit Ryle was to make famous. The philosopher, Wittgenstein wrote, wants to master the geography of concepts: to see every locality in its proximate and its distant surroundings (MS 137, 63a; cf. MS 162b, 6v; MS 127, 99; MS 137, 63a, quoted below p. 000, n. 2). In the early 1930s, he said to his pupils: ‘One difﬁculty with philosophy is that we lack a synoptic view. We encounter the kind of difﬁculty we should have with the geography of a country for which we had no map, or else a map of isolated bits. The country we are talking about is language and the geography its grammar. We can walk about the country quite well, but when forced to make a map, we go wrong’ (AWL 43). In his 1939 lectures he used a similar metaphor: I am trying to conduct you on tours in a certain country. I will try to show you that the philosophical difﬁculties which arise in mathematics as elsewhere arise because we

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ﬁnd ourselves in a strange town and do not know our way. So we must learn the topography by going from one place in the town to another, and from there to another, and so on. And one must do this so often that one knows one’s way, either immediately or pretty soon after looking around a bit, wherever one may be set down. This is an extremely good simile. In order to be a good guide, one should show people the main streets ﬁrst. . . . The difﬁculty in philosophy is to ﬁnd one’s way about. (LFM 44; cf. MS 133, 82)

Presenting such a synoptic view involves reminding us how we use a given problematic expression and how its use meshes with that of others. In so doing, one will also often be describing the bounds of sense — characterizing combinations of words that are excluded from the language. For it is characteristic of philosophy that words are applied beyond the constraints within which they make sense. We think, as it were, that because it makes sense to speak of its being 5 o’clock in London or in New York, therefore it also makes sense to speak of its being 5 o’clock on the sun (PI §350). ‘The aim of philosophy’, Wittgenstein wrote, ‘is to erect a wall at the point where language stops anyway’ (BT 425). A wall is needed because we are constantly tempted (and succumb to the temptation) to transgress the bounds of sense. For although the rules for the use of our words are humdrum and familiar, the limits that they lay down are not always easy to grasp. ‘What can be said in philosophy must always be home-baked [humdrum, ordinary]’, Wittgenstein remarked, ‘the only thing that is not home-baked is the limit of language’ (MS 109 (Vol. V), 16). So we must point out that ‘nothing can be both red and green all over simultaneously’ does not indicate a physical impossibility (unlike ‘nothing can run 100 mph’), let alone a ‘metaphysical impossibility’, but amounts to saying that there is no such thing as being red and green all over, i.e. that ‘is red and green all over’ is a form of words excluded from the language, not a description of a possibility that is impossible. The point of arranging the ‘grammatical facts’ in a readily surveyable form is to dissolve philosophical problems and destroy philosophical illusions. This negative aspect is commonly given a metaphorical therapeutic characterization. The philosopher is the man who has to cure himself of many sicknesses of the understanding before he can arrive at the notions of a sound (healthy) human understanding (RFM 302). What a mathematician is inclined to say about the objectivity and reality of mathematical facts is not a philosophy of mathematics, but something for philosophical treatment. The philosopher treats a question — like a disease (PI §§254f.). There is not a philosophical method, though there are indeed methods, like different therapies (PI §133). In philosophizing we may not terminate a disease of thought. It must run its natural course, and slow cure is all-important (Z §382). The analogy is a good one, although one must not forget that it is only an analogy. Illness prevents our optimal functioning in daily life. By contrast, philosophical worries about the existence of the external world, the existence

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of other minds, or the possibility of an ‘inverted spectrum’ are idle. Philosophical confusions and misconceptions are caused not by infection but by various forms of misunderstanding. They are ‘cured’ not causally, by medicine, but rationally, by arguments, which remind us how we use words, show that the bounds of sense were transgressed, offer us analogies and point out disanalogies, or juxtapose the case in hand with imaginary language-games designed to highlight grammatical features we overlooked. In this way we attain an overview, which produces not health but understanding. The psychoanalytic analogy is also powerful. The philosopher transforms latent nonsense into patent nonsense (PI §§119, 464, 524, see Exg.), just as the psychoanalyst transforms latent emotions into patent ones — for only when they are thus exposed can they be confronted. A primary activity of philosophers is to warn against wrong comparisons, wrong similes that are rooted in our forms of expression, without our being altogether conscious of this. Wittgenstein’s method here resembles the analyst’s: by making us aware of what was unconscious, he tries to render it harmless (MS 109 (Vol. V), 174). Like the analyst, Wittgenstein encourages us to release repressed qualms: A mathematician is bound to be horriﬁed by my mathematical comments, since he has always been trained to avoid indulging in thoughts and doubts of the kind I develop. He has learned to regard them as something contemptible and, to use an analogy from psychoanalysis (this paragraph is reminiscent of Freud), he has acquired a revulsion from them as infantile. That is to say, I trot out all the problems that a child learning arithmetic, etc. ﬁnds difﬁcult, the problems that education represses without solving. I say to those repressed doubts: you are quite correct, go on asking, demand clariﬁcation! (PG 381f.)

There are further similarities. Just as a criterion for correct analysis is the patient’s acknowledgement, so too, ‘One of the most important tasks is to express all false trains of thought so characteristically that the reader says “Yes, that’s exactly what I meant” ’ (BT 410). And just as the analyst expects resistance from the patient, so too in philosophy one of the difﬁculties is ‘the contrast between the understanding of the subject and what most people want to see. Because of this the very things that are most obvious can become the most difﬁcult to understand. What has to be overcome is not a difﬁculty of the intellect, but of the will’ (BT 406). Just as in neurotic disorders there are obsessions, so too in philosophical confusions there is an obsession with certain words, turns of phrase, pictures and an obsessive insistence that things must be thusand-so (AWL 98f.). And just as jokes are psychoanalytically revealing, so too jokes are grammatically revealing — indeed, one could write a philosophy book that consisted of nothing but jokes.11 Again, the analogy is a good one, but it is important to realize that it is but an analogy. Psychoanalysis involves a complex theory about the working of 11

Malcolm, Ludwig Wittgenstein: A Memoir, p. 28.

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the human psyche; Wittgenstein’s philosophy rests on no theory whatsoever. Psychoanalytic problems are produced by childhood traumas, etc., philosophical problems by features of our language and our intellectual dispositions. Psychoanalytic therapy treats patients who cannot function optimally in the stream of life, whereas the Wittgensteinian philosopher treats questions (PI §255) that, according to Wittgenstein, arise when language is idling.12 Philosophical problems are dissolved: solipsism is deﬁnitively shown to be nonsense, the idea of a private language that is implicitly invoked by so many philosophical doctrines is shown to be incoherent, the idea that geometry is a description of the properties of space is exploded (not shown to be false). The resolutions of the problems purport to possess a rational validity which, unlike the resolution of a psychoanalytic illness, is not patient-dependent. So the exercise has a generality absent from psychoanalytic treatment, precisely because the philosopher treats questions. Moreover, in so far as there are arguments in psychoanalysis, they do not show that forms of words that seemed to make sense are actually nonsense. Nor are they designed to get us to grasp the structures of the common, shared grammar of our language, but rather the aetiology of a particular and personspeciﬁc malady. But Wittgenstein, as we shall see, argues that certain suppositions, certain putative doctrines, make no sense. In so doing he clariﬁes the grammar of problematic expressions. And that grammar is the common, shared grammar of our language. It is noteworthy that Wittgenstein became exceedingly angry when Wisdom and Ayer exaggerated the psychoanalytic analogy and attributed it, thus exaggerated, to him13 — they ﬂaunt the keys that they have stolen, he wrote, but they can’t open any locks with them (MS 138, 17a).

4. The difﬁculty of philosophy ‘Why is philosophy so complicated?’, Wittgenstein queried; ‘It ought, after all, to be completely simple.’ To which he answered, ‘Philosophy unties the knots in our thinking, which we have tangled up in an absurd way; but to do that, it must make movements which are just as complicated as the knots. The complexity of philosophy is not in its matter, but in our tangled understanding’ (PR 52). The complexity and difﬁculty of philosophy are a correlate of the complexity of the confusions in which we are trapped and of the difﬁculty of dispelling them. Elsewhere he switched to the geographical analogy to explain the difﬁculty: ‘Teaching philosophy involves the same immense difﬁculty as instruction in geography would have if a pupil brought with him a mass of false and far too 12

This claim may be questioned (see Exg. §132, 1), but it is noteworthy that Wittgenstein thought thus. So from his point of view, this shows the limits of the psychoanalytic analogy. 13 See A. J. Ayer, Part of My Life (Oxford University Press, Oxford, 1978), p. 305. Malcolm reports Wittgenstein twice insisting indignantly that philosophy is a ‘different technique’ from psychoanalysis (ibid., p. 48).

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simple // falsely simple // ideas about the course and connections of the courses of rivers // rivers // and mountain ranges // mountains //’ (BT 423). The difﬁculty of handling philosophical problems is likewise produced by the misguided preconceptions and prejudices that we bring to the problem. We cannot see matters clearly until those preconceptions and prejudices have been identiﬁed and eradicated. Typically, in philosophy, the deepest mistakes are made before debate even begins — in what is taken for granted. So, we may set out to investigate the mental state of knowledge, or of belief, or the mental process of remembering or thinking — and already ‘The decisive movement in the conjuring trick has been made, and it was the very one that we thought quite innocent’ (PI §308). For we think it innocuous to characterize knowledge or belief as mental states, or remembering and thinking as mental processes, carefully leaving it until later to discover exactly what kinds of states and processes they are. But here we already go wrong, since we have a deﬁnite idea of what a state or process is, and that alone commits us to a speciﬁc (and erroneous) way of looking at the issues (see Exg. §308). The debates between idealists and realists, nominalists and Platonists, dualists and behaviourists, mentalists and materialists, which go on for centuries, delude us. We think that the thing to do is meticulously to examine the disagreements between the antagonists and to side with those who muster the best arguments in support of their position. Whereas the correct method is not to examine their disagreements, but to probe for what both sides agree upon, what is taken for granted by all before debate is joined, and challenge that. But to identify the deepest presuppositions common to both sides and to see how they may be questioned requires uncommon insight.14 Stating the rules for the use of a certain philosophically problematic expression may be perfectly simple. Even arranging the rules so as to render them perspicuous relative to a particular philosophical difﬁculty may not be problematic. But doing so may be altogether futile, precisely because of the nature of the misunderstandings. ‘One must start out from error and convert it into truth. That is, one must reveal the source of error, otherwise revealing the truth won’t do any good. The truth cannot force its way in when something else is occupying its place. To convince someone of the truth, it is not enough to state it, but rather one must ﬁnd the path from error to truth’ (GB 119). And ﬁnding the deep roots of the difﬁculty is hard. ‘Because if it is grasped near the surface it simply remains the difﬁculty it was. It has to be pulled out by the roots; and that means that we must begin to think about these things in a new way. The change is as decisive as, for example, that from the alchemical 14

For more detailed examination, see Wittgenstein’s Place in Twentieth-Century Analytic Philosophy, pp. 100–3. Wittgenstein’s strategy here makes it clear why he is so readily misunderstood. In order to recruit him for one side or another in these venerable debates, he has been classiﬁed as an ‘anti-realist’, a ‘linguistic idealist’, a ‘strict ﬁnitist’, etc. What has proved difﬁcult to grasp is that he typically challenged the presuppositions common to both protagonists in these great debates, and accordingly cannot be located on received philosophical maps.

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to the chemical way of thinking. The new way of thinking is what is so hard to establish’ (CV 48; MS 131, 48). Indeed, Wittgenstein noted, once it has been established, the old problems vanish, and may be hard to recapture. This is evident if one reﬂects on the debates about the nature of the proposition at the beginning of the twentieth century (Is Mont Blanc with all its snow-ﬁelds a constituent of the proposition that Mont Blanc is more than 4,000 metres high?15), or on the debate about subsistent entities (Does the golden mountain have to subsist in order for us to be able to say that it does not exist?), or on the logical analysis of facts (Am I a constituent of the fact that I am in pain?) that so preoccupied Cambridge analysts in the 1930s. One may have similar qualms about grammar. If philosophy is primarily an elucidation of grammar with a particular purpose, it ought to be easy. The rules for the use of words are not, after all, that complicated — every child masters them. Nevertheless, grammatical problems are difﬁcult, indeed seemingly ineradicable. That is because they are connected with the oldest thought habits, as it were the oldest pictures engraved into our language itself (BT 423). The subject /predicate forms of our language, coupled with the natural supposition that words stand for things, lead us to suppose that substances are ‘related’ to their properties as the body to its clothing. And because the substantive can be shifted to the predicate position leaving a dummy subject-term, we (like Locke) are prone to wonder what the substance is like when its clothing has been removed. We tend to think that correlative to every substantive there must be an entity, if not a material one then an immaterial or an abstract one. So we think that just as ‘A’s brain’ stands for a biological entity, ‘A’s mind’ must stand for a mental one; and when we are disabused of that error, we jump to the conclusion that the mind is the brain — which we then denominate ‘the mind/brain’. We commonly suppose, when caught in the web of language, that to every adjective there corresponds a property, and wonder what property corresponds to ‘true’ or ‘real’. We think that verbs signify acts or activities, or at any rate doings, and construe meaning something as an activity we perform, and assume that ‘to think’ signiﬁes an activity of the mind as ‘to speak’ signiﬁes an activity of the speaker. When one is caught in the web of words, it is not easy to understand the nature of the problem that bewilders one. Nor is it easy to collect and arrange the grammatical facts in such a way that the problem dissolves. But once it has been properly done, then, like opening a safe once the combination has been found, it is easy to show how the difﬁculty dissolves (BT 417). Finally, giving a synoptic representation of the grammar of a problematic expression is not easy. Not only must the salient grammatical features of the problematic expressions be brought into view, but the misleading analogies and disanalogies must be identiﬁed and rendered harmless. It demands skill, 15

See the exchange in 1904 between Frege and Russell in G. Frege, Philosophical and Mathematical Correspondence (Blackwell, Oxford, 1980), pp. 161, 169.

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insight into intellectual confusion, and understanding of the physiognomy of these deep forms of incoherence; and one must beware of a one-sided diet (PI §593). For the right comparisons are needed to engender realization — realization that one need not think like that at all, that one was held captive by a picture, by a misconceived analogy, by an illusory requirement. Although philosophy has lost its nimbus and is no longer ‘sublime’, it has not lost its depth. The pathos has retreated to the illusions (PI §110).

5. The methods of philosophy It is because ‘a method has been found’ that philosophy has become a skill. To be sure, there is not one single method — but an array of methods (PI §133), guided by an overriding conception of the nature of philosophical problems and the keys to their solution. Many aspects of Wittgenstein’s methods have already been intimated. The following discussion does not aim at completeness — merely at giving an overview of his methods. Local tactical methods (e.g. externalizing alleged mental operations, imagining changes in us or in the course of nature) will not be discussed.16 Above all, the methods of philosophy are descriptive (PI §124). What is described is the use of language. ‘We want to replace wild conjectures and explanations by quiet weighing of linguistic facts’ (Z §448). Wittgenstein held that the deepest error of philosophers of his day was that they attend to the forms of words rather than to their uses (LA 2). The classiﬁcations of philosophers are like classifying clouds by their shapes (MS 105 (Vol. I), 36). Moreover, it is characteristic of philosophers to misuse words in their reﬂections. ‘When philosophers use a word and enquire after its meaning, one must always ask oneself: Is the word ever actually used like this in the language for which it was made. One will mostly ﬁnd that it isn’t so, and that the word is being used contrary to its normal grammar’ (MS 109 (Vol. V), 246). His task, he said, was to bring words back from their metaphysical uses (or misuses) to their everyday use (PI §116; see Exg. for what counts as a metaphysical use). To speak of the world as consisting of facts, or of facts as consisting of objects in concatenation, for example, is not a ‘special technical use’ of the word ‘fact’, but an incoherent misuse of the word. However, even when the metaphysician can insist that he is using a familiar word in a special, extended ‘metaphysical’ sense, he will typically cross the new use with the old, draw illegitimate inferences, and talk nonsense. Often, even when he candidly admits that his usage is a technical extension of ordinary use (as the author of the Tractatus presumably would have admitted with regard to his use of ‘name’ and Frege would have admitted with regard to ‘object’), once the theory-driven 16

For a detailed survey of Wittgenstein’s methods in philosophy of mind, see Volume 4, ‘Methodology in philosophical psychology’.

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preconceptions behind the extended use become transparent, the temptation to adopt it vanishes. Philosophy only describes language. Contrary to what Frege and Russell thought, it is not part of its task to interfere with the actual use of language, to reform our language or replace it by an allegedly improved, regularized one (PI §133). For the problems of philosophy stem from failure to grasp the articulations of existing grammar. Replacing this with a (fragment of a) so-called ideal language will not resolve these problems, but merely sweep them under the carpet. If we are puzzled, as Berkeley was, that warm water can feel hot when one puts a cold hand in it, and feel cold if one plunges one’s other, hot, hand in it — one’s puzzlement is not resolved ( pace Carnap and his method of explication) by being told to replace the thermal concepts of warmth, cold and hot by the scalar concept of temperature. That merely robs us of our puzzlement without resolving it. Describing the use of words, in the sense pertinent to Wittgenstein’s investigations, is a matter of specifying or stating how words are used in the practice of speaking the language. Usage sets the standard of correct use; so the investigation is a normative one. We must remind ourselves how we use the problematic expressions — that is to say, what counts in the practice of speaking our language as a correct use. So we are, in effect, stating rules (or fragments of rules) for the use of the expression (for discussion of Wittgenstein’s conception in this matter, see Volume 2, ‘Rules and grammar’). These may be stated or referred to in the formal, metalinguistic, mode: e.g. ‘The grammar of the word “knows” is evidently related to that of “can”, “is able to” ’ (PI §150), or ‘The rule which shows us that the word “is” has different meanings in [“the rose is red” and “twice two is four”] is the one allowing us to replace the word “is” in the second sentence by the sign of equality and forbidding this substitution in the ﬁrst’ (PI §558), or ‘It is correct to say “I know what you are thinking”, and wrong to say “I know what I am thinking” ’ (PI p. 222/189), or ‘It makes sense to say about other people that they doubt whether I am in pain; but not to say it about myself ’ (PI §246). Sometimes, however, Wittgenstein speciﬁes grammatical rules by means of ‘grammatical propositions’ couched in the material mode, e.g. ‘I can only see, not hear, red and green, — but sadness I can hear as much as I can see’ (PI p. 209/178), ‘One can mistrust one’s own senses, but not one’s own belief ’ (PI p. 190/162). Occasionally, Wittgenstein makes remarks that are epitomes of lengthy grammatical investigations, which typically intimate rather than state grammatical rules, e.g. ‘It is in language that expectation and its fulﬁlment make contact’ (PI §445), which provides a crucial part of his resolution of the problem of intentionality, rejecting the position embraced in the Tractatus that the proposition and the fact that makes it true make contact, as it were, between language and reality. This enigmatic rejection of his earlier view intimates that the phrase ‘the expectation that p’ is, mutatis mutandis, intersubstitutable with the expression ‘the expectation that is satisﬁed by the occurrence of the event that p’,

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these being simply two different ways of referring to the same expectation (cf. PG 161f.). Similarly ‘An “inner process” stands in need of outward criteria’ (PI §580), occurs, in its argumentative context (see Exg. §580), as part of an ironic repudiation of the idea that believing is an inner process. But it intimates that expressions that do signify ‘inner processes’ (e.g. talking to oneself in the imagination), or indeed ‘inner states’ (e.g. being in pain), are grammatically bound up with behavioural criteria for their application in the thirdperson case — a matter that was laboriously clariﬁed by the lengthy arguments against the intelligibility of a ‘private language’. Much more commonly, however, Wittgenstein merely nudges us in the direction of bringing to mind the rules, and differences between rules, with which we are perfectly familiar. For example, to disabuse us of the idea that an ability is a state, he queries ‘When are you able to play chess? All the time? or just when you are making a move? And the whole of chess during each move? — How queer that being able to play chess should take such a short time, and a game so much longer!’ (PI p. 59/50n.). To disabuse us of the thought that ‘to mean something by something’ is an activity-verb, he queries ‘Tell me, what was going on in you when you uttered the words . . . ?’ — and notes that the answer is not: ‘I was meaning . . .’! (PI §675). His typical argumentative strategy is to ﬁre questions at his readers to move them away from the mistaken grammatical paradigm to which they cleave and towards an overview of the grammar of the expressions that are causing trouble. He rarely tries to paint a comprehensive picture of the grammatical landscape that he has in view. Rather, he typically induces us to look for ourselves, reminding us of aspects of use (e.g. ‘We do say . . . , but we also say . . .’ (PI §183),) and warning us, usually by means of pointed questions, against confusing ditches with rivers, follies with ruins, and mirages with oases. In the endeavour to get clear about the use of a word, it is often fruitful to ask how one was taught it — not because we are engaged in learningtheory or child psychology, but because reﬂection on this helps to destroy misconceptions (LA 2). The primitive language-games with which the child begins often provide illuminating ‘centres of variation’ from which to view mature uses. This is exempliﬁed by Wittgenstein’s reﬂections on how one would teach a child the use of the words ‘hurts’ and ‘a pain’ (i.e. as a partial substitute for crying in pain), or the use of ‘a dream’ and ‘to dream’ (not by being shown a dream, but (inter alia) by being taught to preﬁx ‘I dreamt’ to ‘I was being chased by a monster’), or how the child learns the use of ‘I’m going to’ (not by ‘identifying an intention within one’, but as heralding an action: when one says ‘I’m going to . . .’, then one goes on to . . . ), and so forth. Of course, reminding us of the way we use words, ‘tabulating rules’ (WWK 184), may not be the end of the matter, but it is the beginning. We need to attain an overview of the grammar of the expression that troubles us, to bring to mind — where relevant — the multitude of paths that lead off from it in every direction (PI §534). We need to apprehend — where pertinent — the

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analogies in use between it and other expressions that may look very different from it (e.g. between arithmetical equations and rules), and the disanalogies in use between it and expressions that look akin (e.g. ‘I have a pain’ and ‘He has a pain’). If I correct a philosophical mistake and say that this is the way it has always been conceived, but this is not the way it is, I always point to an analogy // . . . I must always point to . . . // that was followed, and show that this analogy was incorrect.17 // . . . I must always point to an analogy according to which one had been thinking, but which one did not recognize as an analogy. (BT 409)

To sharpen our eye to formal connections, Wittgenstein often invents imaginary language-games to put beside our own to highlight otherwise unnoticed features, to illuminate the ways in which our language-games depend for their point upon background conditions, or to show that different conceptual structures are perfectly intelligible. A different method, only mentioned in the Investigations, but elsewhere advocated, is the invention of different notations. When Frege and Russell introduced the epsilon notation for class inclusion, a difference in the use of ‘is’ was brought out vividly, in a way in which it is not brought out in our notation by the difference between ‘is’ and ‘equals’. Wittgenstein mentions his own Tractatus invention of the notation that dispenses with the identity-sign, which helps rid one of puzzlement about identity-statements (AWL 98f.). He might also have mentioned his invention of the T/F notation, which demonstrates the dispensability of the logical connectives in the propositional calculus, and rids one of the temptation to construe them as names of logical entities (e.g. of functions). The generic method of philosophy, as advocated by Wittgenstein, is to investigate sense, not truth. His concern is with what it makes sense to say — in order to clear up confusions exhibited in saying things that seem to make sense but do not. The task of the philosopher is not to show that solipsism or idealism are false, but to show that they are, at best, recommendations to adopt a new notation, and at worst, incoherent transgressions of the bounds of sense. He wrote: I am, as it were, collecting meaningful sentences about toothache — this is the characteristic activity of a grammatical investigation. I collect not true, but meaningful sentences, and that is why this approach is not psychological. (One would like to call it ‘metapsychological’.) Philosophy constantly collects material, consisting of sentences, without worrying about truth or falsehood; only in the case of logic and mathematics is it concerned only with ‘true’ sentences. (MS 107 (Vol. III), 285f.)18

The negative, destructive task of philosophy is the eradication of conceptual illusions and confusions. Philosophizing, he wrote, is rejecting false arguments 17 18

Wittgenstein had qualms about the word ‘incorrect’ here. For an explanation of the latter remark, see Volume 2, ‘Grammar and necessity’, sect. 3.

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(BT 409). This, to be sure, is done by argument (LWL 63). It has been said that there are no arguments in Wittgenstein’s later philosophy. That is misleading. What is true is that in arguing against common philosophical doctrines, such as idealism or solipsism in metaphysics, Platonism, formalism or intuitionism in philosophy of mathematics, dualism or behaviourism in philosophy of mind, Wittgenstein does not show these doctrines to be false. He shows them to be nonsense. So his arguments cannot be presented in the form of a logically valid deductive argument, the conclusion of which is, for example, that solipism is false. Nor can they be presented in the form of a reductio ad contradictionem (the form of argument logicians misleadingly refer to as a reductio ad absurdum) one of the premisses of which is, for example, the solipsistic claim ‘Only my experience is real’, and the conclusion of which is a formal contradiction. But it does not follow that there are no arguments. In the ﬁrst place, it is not evident that there cannot be deductively valid arguments in philosophy, the premisses of which spell out conditions of sense and the conclusion of which is that a given form of words lacks sense (since it fails to accord with the conditions of sense).19 Such an argument does not (absurdly) prove that a possibility is impossible, it proves that a form of words is excluded from the language. Secondly, the idea that deductively valid argument is the only kind of respectable argument is wrong. To argue is to provide reasons for or against something, and these reasons may be as varied as one pleases. Wittgenstein provides a multitude of reasons to show that the positions he assails are incoherent. So they are literally informal reductio ad absurdum arguments (but not in the logicians’ sense). It would be quite mistaken to think that he was the ﬁrst philosopher to attack his predecessors as propounding nonsense — for this was a major plank in Kant’s platform. Kant too argued that his antagonists transgressed the bounds of sense, attempted to apply concepts beyond the sphere of their intelligible application. Further, Wittgenstein offers reasons for observations he makes about grammar and grammatical structures, e.g. reasons why a sample, invoked in an ostensive deﬁnition, should be considered as belonging to grammar, or reasons why a sensation cannot fulﬁl (there is no such thing as a sensation’s fulﬁlling) the role of a deﬁning sample, or reasons why a mathematical equation should be characterized as a rule.

6. Negative corollaries Wittgenstein insisted, again and again, that there are no theories in philosophy and no hypotheses. There are no theses and no explanations. This has occasioned puzzlement and indignation, as well as misintepretation. 19

We should also note that a mathematician’s impossibility proof, e.g. that one cannot square a circle or trisect an angle with a compass and rule is, in effect, a proof that a certain form of words has no sense (viz. ‘a squared circle’ or ‘to trisect an angle with compass and rule’). For discussion of Wittgenstein’s reﬂections on the trisection problem, see Exg. §§334, 463.

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The paradigm of a theory is provided by scientiﬁc theories — of gravity, relativity, electricity or evolution. Theories involve the construction of hypotheses which may be more or less correct, that are modiﬁable in the light of new facts, and that achieve greater or lesser accuracy in predictions. In physics, theories typically give an idealized description of natural phenomena, representing light rays as straight lines or bodies as point-masses. They abstract from secondary factors — e.g. disregard gravitational forces of distant stars in constructing terrestrial mechanics. And successful theories make new discoveries — about the constitution of matter, for example, or the nature of radiation. It is in this sense of ‘theory’ that Wittgenstein insists that there are none in philosophy. There are no hypotheses in philosophy, since philosophy moves around in the domain of the meaning-determining rules of grammar. It cannot be a hypothesis that a form of words one understands and uses correctly makes sense. The meaning of an expression is given by explanations of meaning. The explanations of the meanings of expressions are standards for their correct use the giving of which constitute criteria of understanding. There is nothing hypothetical about these, any more than it is a hypothesis of a competent chess-player that the chess queen moves thus-and-so. Of course, the rules of language are far more complex and varied than the rules of chess, and it is not always easy to bring the relevant ones to mind. Care is needed; one must trawl wide and deep for diverse examples. It is possible to err here, to forget one aspect or another of one’s usage. That is why philosophy is a matter of recollection — we remind ourselves and our interlocutor that we really do use a given word thus-and-so (BT 419). There can be no room for predictions in philosophy, and no room for approximations to sense. For deviation from what makes sense is one form or another of nonsense. Nor is there any room in philosophy for idealization — for the problems of philosophy stem from our existing concepts, and if we idealize these, we obtain different concepts and pass over the difﬁculties which trouble us. One can reform concepts for practical or for theoretical purposes in the sciences — not in philosophy. (But this is far from being a prohibition on drawing new or more reﬁned distinctions for purposes of philosophical clariﬁcation.) It is a cardinal error of the metaphysical endeavours of philosophers to construct metaphysical theories on the model of science. For metaphysicians try to explain conceptual phenomena (typically misconstrued) on the model of scientiﬁc explanation. They conjure into existence weird and wonderful things, Platonic Forms, Leibnizian monads, an Unmoved Mover or Omnipercipient Inﬁnite Mind, noumena, the Absolute, etc., in order to explain how something can be as it is, or how we can do something we do. The Tractatus too exempliﬁed this tendency. For Wittgenstein had tried to explain how a proposition can be false but meaningful, how we can think what is not the case, by postulating the existence of simple sempiternal objects. They seemed to be the sine qua non for the possibility of representation by means of language, indeed

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implicitly presupposed by logic — a curious mimicking of a scientiﬁc inference to the best explanation. But this parody of the procedures of science is misconceived. Scientiﬁc hypotheses are veriﬁed by experiments and have experimental consequences, lead to new discoveries, enable predictions and technological advances. Metaphysical and ontological postulates are no more than painted stage-props to a misconceived account of the workings of our conceptual scheme. One aspect of the metaphysical syndrome is a craving for explanation. But in the sense in which the sciences explain phenomena, there are and can be no explanations in philosophy. ‘Every explanation is an hypothesis,’ Wittgenstein remarked (GB 123), thinking of causal explanations in the sciences. Apropos Frazer’s explanations of magic, he wrote: ‘I believe that the attempt to explain is already therefore wrong, because one must only correctly piece together what one knows, without adding anything, and the satisfaction being sought through the explanation follows of itself ’ (GB 121). It is part of Wittgenstein’s ‘morphological method’ (see ‘Surveyability and surveyable representations’, sect. 3) that philosophical clariﬁcation is not hypothetical or theoretical, but descriptive. This excludes explanation on the model of the sciences. ‘We must know what explanation means. There is a constant danger of wanting to use this word in logic [philosophy] in a sense that is derived from science’ (BT 418). To be sure, there is a broader sense of explanation, of which the hypotheticodeductive and causal explanations of the sciences are merely a special case. In this sense an explanation is what renders intelligible something that was puzzling. So there is a licit sense of explanation in which Wittgenstein does explain things — he clariﬁes problems and resolves puzzlement. He was aware of this. In a playful passage he wrote (The man who says that one can’t step twice into the same river says something false; one can step twice into the same river. — And an object sometimes ceases to exist when I cease to look at it, and sometimes not. — And we do know, sometimes, what colour another person sees when he observes a given object, and sometimes we do not.) And this is what the solutions to all philosophical difﬁculties look like. Our answers, if they are correct, must be ordinary and trivial. — For the answers, as it were, make fun of the questions. (TS 220, §111)

In a later draft (TS 238, §126) he added: ‘But not the explanations, which make the problem intelligible.’ Grammatical explanations, reminders of the rules for the use of words, are, of course, licit — indeed, part of the method. So too, it is patent that Wittgenstein explained, in depth and detail, the sources and nature of philosophical confusions. Just as there are no explanations on the model of science in philosophy, so too there are no discoveries (WWK 183; MS 109 (Vol. V), 298). There cannot be hidden rules of grammar that determine the sense of expressions we

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understand. For were they ‘hidden’, awaiting discovery, they could not fulﬁl the function of rules, i.e. determine the senses of expressions in use, constitute standards of correctness, and guide us in the correct use of our words. ‘Everything lies open to view’, and what is hidden ‘is of no interest to us’ (PI §126). In philosophy, if it is news — a discovery — then it is wrong (LWL 26, 35). The response to science is, as it were, ‘Goodness me; who would have thought of that!’. The response to philosophy is: ‘Yes, of course; I should have thought of that!’. The misunderstandings that concern philosophy do not arise through lack of information (BT 416). (One must be careful here, since Wittgenstein brings us to realize much that we never realized before. In that sense, his philosophical investigations might be said to add to our knowledge — but not to our knowledge of the world. For what we come to realize are not new facts about the world, but grammatical connections and relationships, similarities and differences, analogies and disanalogies, that had not struck us before.) Finally, Wittgenstein emphasized that there are no theses in philosophy. This has occasioned bafﬂement. For surely Wittgenstein argues that idealism is nonsense, that there can be no such thing as a private language, that Platonism and Intuitionism are misconceived, and so forth. Are these not theses? No, that is not what he meant. The remark seems to have been made with the propositions of the Tractatus in mind, probably with reference to Waismann’s ‘Thesen’, which were circulating among the members of the Vienna Circle. These were a simpliﬁed account of the main contentions of the Tractatus, updated in the light of Wittgenstein new ideas (e.g. about veriﬁcation). It was of these that Wittgenstein said ‘a rehash of such theses is no longer justiﬁed’ (WWK 184). So remarks such as ‘Reality consists of facts, not of things’, ‘A state of affairs is a combination of elements’, and ‘The sense of a thought is the existence or non-existence of states of affairs’ count as theses. This suggests that a ‘thesis’ is an essentialist claim (construed de re rather than de dictu) concerning how things are (hence exempliﬁed by the metaphysical pronouncements of the Tractatus, and Waismann’s rehash of them in his ‘Thesen’ (WWK 233–61)). Theses in effect say that things must be thus-and-so — which Wittgenstein characterizes as ‘dogmatism’. It appears to be such statements above all that Wittgenstein excludes from philosophy. However, he does say that if one wanted to advance theses in philosophy, then everyone would have to agree with them (PI §128). This is a paradoxical remark, but some light is shed on it by a discussion with Waismann: If there were theses in philosophy they would have to be such that they do not give rise to disputes. For they would have to be put in such a way that everyone would say, Oh yes, that is of course obvious. As long as there is a possibility of having different opinions20 and disputing about a question, this indicates that things have not 20

For discussion of the elimination of opinions in philosophy, see Exg. §128.

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been expressed clearly enough. Once a perfectly clear formulation — ultimate clarity — has been reached, there can be no second thoughts or reluctance any more, for these always arise from the feeling that something has now been asserted, and I do not yet know whether I should admit it or not. If, however, you make the grammar clear to yourself, if you proceed by very short steps in such a way that every single step becomes perfectly obvious and natural, no dispute whatsoever can arise. (WWK 183)

So, a perspicuous statement of a grammatical rule does not count as a thesis. And descriptions of grammar are not dogmatism either. For to remind us that we do use words thus-and-so is not to make any essentialist claim. And, of course, if someone contests the grammatical description, that need not matter either. All that follows is that he means something different by the word in question — and we should ask him to explain what he does mean: when we are talking about negation, for instance, the point is to give the rule ‘~ ~ p = p’. I do not assert anything. I only say that the structure of the grammar of ‘~’ is such that ‘p’ may be substituted for ‘ ~ ~ p’. Were you not also using the word ‘not’ in that way? If that is admitted, then everything is settled. And this is how it is with grammar in general. The only thing we can do is tabulate rules. If by questioning I have found out concerning a word that the other person at one time recognizes these rules and, at another time, those rules, I will tell him, In that case you will have to distinguish exactly how you use it; and there is nothing else I wanted to say. (WWK 184)

However, one might object that surely Wittgenstein does propound theses. For he tells us that expectation and its fulﬁlment make contact in language, or that inner processes stand in need of outer criteria, or that ‘I know that I have a pain’, in the mouth of a philosopher, is nonsense. And these points have engendered endless arguments. That is correct. However, as noted above, it is important to locate these observations in their argumentative contexts and to note that these are, directly or obliquely, grammatical assertions. The ﬁrst remark is a compact repudiation of a Tractatus conception, coupled with an intimation of a grammatical rule, which, once stated explicitly, can hardly be denied: namely, that e.g. ‘the expectation that A will come’ = ‘the expectation that is satisﬁed by A’s coming’. The second is, in the context of a discussion of belief (PI §§573–80, see Exg. §580), an ironic invocation (since belief is not a process at all) of a grammatical connection between psychological expressions that are applied in the ﬁrst-person case without any grounds whatever, but are linked, in the third-person case, with observational grounds of application (criteria). Elaborate clariﬁcations of this grammatical nexus are given in the ‘private language’ arguments, where Wittgenstein shows that the consequence of severing this nexus would be to deprive the ﬁrst-person use of any content whatsoever. The third example is intended to be a straightforward grammatical observation, although it is supported by quite extensive grammatical considerations that scrutinize the general grammatical requirements for the non-vacuous preﬁxing of the epistemic operator ‘I know’ to a sentence.

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So these propositions, and others like them, cannot be characterized as theses. It is also noteworthy that Wittgenstein does not invoke them as premisses for further arguments. So nothing rests on them. If they are contested, then we (or Wittgenstein) must go back a few steps, and patiently explain further. Could the expectation that N will come to dinner be satisﬁed by anything other than N coming to dinner? What would it be? What would count as someone’s having a concept of an inner process for which there are no behavioural criteria? Would we understand what he was talking about? Would he understand? If we have a use for ‘I know that p’, it is because it is informative, excluding a possibility: namely, its being the case that p and my not knowing it. But is this so in the case of ‘I have a pain’? — And the grammatical elucidation may continue.

7. Misunderstandings Informing philosophers that they have misunderstood the nature of their investigations for the past 2,500 years was never likely to win their immediate approval. Telling them that their subject is not even a cognitive discipline and that philosophers do not add to the sum of human knowledge about the world around them was sure to enrage them.21 Numerous misunderstandings ensued. Some critics thought that Wittgenstein had trivialized a profound subject. Others could not understand why a philosopher, any more than a scientist, should have the least concern with how the man on the Clapham omnibus uses words, and could not see why the philosopher may not introduce his own special technical terminology as all theorists may and do. Seizing upon the remark that philosophy leaves everything as it is, many were horriﬁed at this apparent declaration of the impotence of philosophy and its irrelevance to everything important. Some of these concerns will be addressed here, others are discussed in Wittgenstein’s Place in Twentieth-Century Analytic Philosophy, ch. 8. Philosophy only states what everyone admits. (PI §599) If one tried to advance theses in philosophy, it would never be possible to debate them, because everyone would agree with them. (PI §128) What we ﬁnd out in philosophy is trivial; it does not teach us new facts, only science does that. (LWL 26)

One may well ask, ‘Why do philosophy then?’ The subject seems to have been reduced to trivialities. But that is mistaken. Philosophy has indeed ‘lost its nimbus’. It is not a sublime investigation into the essence of all things. But philosophy has lost neither its depth nor its importance. The depth lies in the 21

For discussion of Russell’s reaction, see Wittgenstein’s Place in Twentieth-Century Analytic Philosophy, pp. 228f.

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confusions and misconceptions which it is the task of philosophy to eradicate, and the importance lies in their signiﬁcance in philosophy, in science and in daily life. The confusions are deep, precisely because ‘their roots are as deep in us as the forms of our language’ (PI §111). The problems of philosophy are mischaracterized as pseudo-problems (indeed, it was in the Tractatus, not the Investigations, that Wittgenstein used this derogatory phrase which Carnap subsequently made famous). They are perfectly genuine problems (puzzling questions, matters for inquiry, difﬁculties) — only not empirical or theoretical ones. They are problems that need to be dissolved; or given a ‘grammatical’ answer. They are, indeed, deep, but not deep problems about a special subject matter (e.g. the ‘logical structure of the world’, the ‘deep structure of language’, the ‘machinery of the mind’). The idea that philosophy is impotent, that it is a mere idle amusement, was far removed from Wittgenstein’s mind, and diametrically opposed to the conception of philosophy he was advocating. The remark that philosophy ‘leaves everything as it is’ (PI §124) was misinterpreted. In context, it says that philosophy leaves grammar as it is, that it is not the task of philosophy to reform language, to produce an ideal language, as Frege and Russell had supposed. This is not, in any sense, an admission of the impotence or pointlessness of philosophy. Indeed, in a profound sense, Wittgenstein is the ﬁrst to give philosophers an adequate warrant to interfere in the sciences. For just because ‘the philosopher is not a citizen of any community of ideas’ (Z §455), he has, as an outsider, the right to criticize members of communities of ideas when they transgress the bounds of sense. Although philosophy can no longer aspire to be the Queen of the Sciences, she remains the Tribunal of Sense — that is, the systematic critic of conceptual confusion. It is, to be sure, not the task of the philosopher to interfere with the proofs of mathematicians; but what mathematicians say about their proofs may well be grist for philosophical mills. And far from leaving mathematics as it is, a good philosophy of mathematics ‘will have the same effect on the growth of mathematics as sunlight has on the growth of potato shoots. (In a dark cellar they grow yards long.)’ (PG 381). Similarly, ‘in psychology there are experimental methods and conceptual confusion’ (PI p. 232/197) and the eradication of such conceptual confusions is the task of Wittgenstein’s philosophy of psychology. Because Wittgenstein stressed that the problems of philosophy are grammatical, it seemed to some of his readers that he was claiming that philosophy is about language. So it seemed to them that he was arguing that philosophy is a branch of linguistics, or that philosophy is ‘merely’ about words, or that his philosophy canonizes the ordinary use of words. This too is misconceived. The problems of philosophy concern not what is actually the case (that is the province of science) but what can be the case — that is, what it makes sense to say. What it makes sense to say is determined by the rules of grammar. But that does not make philosophy more about the rules of grammar than it is about the nature of thinking, imagination, consciousness, self-consciousness, memory,

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etc. Nor does it mean that Wittgenstein wants to talk only about words (PI §370). It is correct that grammatical misunderstandings and misuses of words are a great source of philosophical confusions, but, as has been argued above, these are not the only sources. Moreover, there is nothing trivial about language and its uses, or about the confusions into which we are led through our failure to have an overview of a domain of grammar that causes trouble. We are the kinds of creatures we are because we possess a language. Our distinctive capacities, e.g. our rationality, our knowledge of good and evil, and our possession of a conscience, our self-consciousness, our capacity for apprehension of necessary truths, are all functions of the fact that we are language-using creatures. There is no ‘merely’ about the grammatical problems that concern philosophy. Nor are the problems inconsequential. Conceptual confusions wreak havoc with scientiﬁc and social-scientiﬁc research programmes — the history of science is littered not only with mistaken theories, but also with the wreckage of misconceived theories rooted in conceptual incoherences — in physics, neuroscience, psychology, empirical linguistics, economics, etc. Nor are conceptual confusions merely innocent excrescences on the thought of Everyman in his home-baked reﬂections on morality, law and politics. Philosophy may have lost its halo, but it has found a vocation. Wittgenstein’s grammatical investigations are unlike those of a philologist (BT 413). The rules that interest him are the very kind of rule the linguist ignores (e.g. that one may not afﬁx ‘north-east of ’ to ‘the North Pole’ or to ‘the South Pole’ (PLP 135f.) or that ‘I don’t know what I want’, unlike ‘I don’t know what he wants’, is an expression of indecision, not of ignorance). Wittgenstein is concerned with grammatical rules only in those domains in which people are tempted to transgress them and consequently fall into conceptual confusion (BT 425). He is interested in ‘ordinary language’, by contrast with the technical language of the sciences and of mathematics, only to the extent that the problems he is dealing with arise in respect of matters expressed in ordinary non-technical language. But when he discussed transﬁnite arithmetic, his concern was not with ordinary language but with the technical language of mathematicians. And when he was investigating problems in the philosophy of logic, e.g. the relationship between the quantiﬁers in the predicate calculus and their natural language correlates, he was concerned not only with the use of ‘all’, ‘some’, etc., but also with the use of ‘(x)’ and ‘(∃x)’ in the technical language of the calculus. Did he hold that one may not introduce technical terminology into philosophy? He certainly did not think that there was any deep need for it. The Tractatus had been rich in technical terms (e.g. ‘pictorial form’, ‘representational form’, ‘logical form’, ‘pictorial structure’), but, as he subsequently realized, this is not really necessary (BT 420). He placed no prohibition on introduction of new terms, and did indeed introduce a few himself (e.g. ‘family-resemblance concepts’, ‘language-games’, ‘genuine duration’), but felt no need for many. The distinctions one needs to draw in the domains of

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language that Wittgenstein investigated can by and large be drawn without the encumbrance of technical terms. Why did he think that we must slavishly follow ordinary use? Why are scientists at liberty to use terms in a new sense, which does not conform to the usage of the man on the Clapham omnibus, while the philosopher is prohibited from so doing? The questions are misleading. It is true that Newton’s use of ‘force’ and ‘power’ deviates from that of the ordinary speaker. But Newton was constructing a theory. His redeﬁnitions of terms had a theoretical warrant, and were not likely to get confused with the ordinary extra-theoretical uses of these terms. Had his theory proved wrong or useless, the terminological innovations and extensions would have been rejected along with the false theory. In philosophy, by contrast, we are not concerned with constructing theories (in the sense in which science is), but with dissolving conceptual problems that involve confusions in the use of terms (CV 44). So it is those terms we must investigate, and not replace them by others — which merely evades the difﬁculty (as does Carnap’s method of explications). This is not slavishly following ordinary use, but carefully investigating it and clarifying those aspects of the grammar of the terms that are giving trouble. Extending existing expressions in philosophy, unlike science, is not driven by conjectures or theories about natural processes. No fact justiﬁes it. And it risks not only evasion, but also confusion. For since the extended use has no role in a theoretical structure, there is far greater chance that the extended use will become inadvertently crossed with the old use, and inferences that can be drawn only from one will be mistakenly drawn from the other. Wittgenstein has been accused of a philistine defence of common sense. This is wrong. He insisted that there is no common-sense answer to philosophical problems. Philosophical problems do not arise for common sense. The common-sense answer to Zeno’s puzzlement ‘How can Achilles possibly overtake the tortoise?’ is ‘By putting one foot down after the other’ — and that will help no one. But, as we have seen, such answers, if offered by a philosopher, merely make fun of the questions (TS 220, §126, quoted above). Rather, what needs to be done is to ﬁnd the sources of the confusions that lead sane and intelligent people to be bafﬂed by Zeno’s Paradox or the Cretan Liar Paradox; or to become bewildered, as Augustine was, about how we can possibly do something we all do constantly, namely measure time; or to think objects cannot exist unperceived (that their esse is percipi); or that we can never really know what someone else is thinking or feeling; or that the mind must be identical with the brain. It is here, in the entanglements in the web of language, that the real philosophical problems lie. Disentangling them has nothing to do with ‘common sense’, even in those cases where the ﬁnal answer is one which comes within the ambit of common sense and with which common sense would agree (BB 48, 59; AWL 108f.). It has been said that Wittgenstein was not a systematic philosopher — even that his conception of philosophy precludes the idea of systematic philosophy. This is misleading, at least if it suggests that Wittgenstein, like Lichtenberg or

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Pascal perhaps, gives us no more than collections of scintillating aperçus. It is certainly true that Wittgenstein does not offer us a systematic theory of anything; he does not offer us an unsystematic theory either, since he denied the intelligibility of theories in the domain of philosophy. However, his remarks in the Investigations are anything but haphazard, unsystematic collections of insights. Not only are they arranged with meticulous care, with a particular argumentative goal in mind, they also explore, in a thoroughly systematic fashion, the sources of error and illusion. If being systematic, with respect to philosophical problems, consists in thoroughness, in exploring a great range of conceptual connections, in examining analogies and disanalogies with related concepts, in investigating the numerous pitfalls that might lead one astray, then Wittgenstein was systematic.22 He travelled ‘over a wide ﬁeld of thought, criss-cross in every direction’ (PI, Preface), sketching the landscape from numerous different directions. The resultant sketches conjunctively give us an idea of the landscape — as an album does. On the other hand, it is also true that he does not give us, or on the whole try to give us, paintings. He does not supply systematic surveys of the subjects he deals with, in the sense of surveying the grammar of expressions in, for example, chapters on understanding, thinking, imagining, the meaning of a word, the meaning of a sentence, and so forth. But he often supplies, in his multitudinous scattered remarks, the materials for such synopses (see ‘Surveyability and surveyable representations’, sect. 4). It is also true that he rarely spells out his arguments in detail. The batteries of questions that he bombards us with are often designed to get us to think our way through to the conclusion. He often shoots an arrow at his target, leaving it to the reader to see why that was the target, and that the arrow has hit it. This gives his writing formidable evocative power and richness — but also great potentiality for misunderstanding and misinterpretation.

8. Retrospect: the Tractatus and the Investigations It is often said that there are deep continuities between the conception of philosophy advocated in the Tractatus and that advanced in the Investigations. The question of the extent of continuity is a delicate one. Any judgement on the matter must distinguish the practice of philosophy in the Tractatus from the programme for future philosophy which the book proposes. It is true that many of the propositions concerning philosophy in the Tractatus can be applied to the Investigations; but often these are, if so applied, merely old bottles with new wine. And it is important not to feign that the wine is vintage Tractatus. 22

It is instructive to compare Wittgenstein with Quine, often thought to be a systematic thinker. There are few major topics in Quine’s philosophy of logic and language that are not also discussed (and dealt with in a very different way) by Wittgenstein (see Wittgenstein’s Place in Twentieth-Century Analytic Philosophy, ch. 7). But there are numerous topics in Wittgenstein’s philosophy of logic and language that are not dealt with in Quine’s.

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Where the continuity seems indisputable and direct is in respect of negative claims. From his earliest reﬂections, Wittgenstein turned his face against the Russellian conception of philosophy as an extension of science. Philosophy is not one of the natural sciences (TLP 4.111), and Russell’s method in his ‘Scientiﬁc Method in Philosophy’ is merely a retrogression from the method of physics (NB 44).23 Equally, like Frege, he insisted that ‘Psychology is no more closely related to philosophy than any other natural science’ (TLP 4.1121) — thus repudiating nineteenth-century German psychologism (and much of the British empiricist tradition). On these demarcation issues he never changed his mind. When it comes to the methodology of the practice of philosophy in the book, however, matters are different. As we have seen, he had a sublime conception of philosophy as an investigation into the a priori order of the world. This conception he repudiated completely. What was peculiar about it, and what made it unique among traditional sublime conceptions of the subject, was not just its insistence that only logico-linguistic investigations can reveal the essence of things, but further, that, according to the ‘main point’ of the book, i.e. the ‘theory of what can be expressed ( gesagt) by propositions — i.e. by language’ — and of what can only be shown by language (CL 68), none of the results of these investigations can, strictly speaking, be said. Hence too, he criticized past philosophical works as being not false but nonsense. They transgress the bounds of sense. ‘Most of the propositions and questions of philosophers arise from our failure to understand the logic of our language’ (TLP 4.003). This observation Wittgenstein could apply to past philosophers even after the transformation of his views in the 1930s — but with a crucial difference. His conception of ‘the logic of our language’ changes dramatically. As indeed did his conception of metaphysics. For ineffable metaphysics, mirrored in the logical syntax of language, was just as much an illusion as effable metaphysics. However, when we turn to the programmatic observations concerning the future course of philosophy, matters become less clear. Philosophy aims at the logical clariﬁcation of thoughts. Philosophy is not a body of doctrine but an activity. A philosophical work consists essentially of elucidations. Philosophy does not result in ‘philosophical propositions’, but rather in the clariﬁcation of propositions (‘Klarwerden von Sätzen’). (TLP 4.112) 23

This remark on NB 44 appears to be a comment on ch. 3 of Russell’s Our Knowledge of the External World as a Field for Scientiﬁc Method in Philosophy. So too are the remarks there on scepticism (compare NB 44 with OK 70, where Russell holds scepticism to be an access road to philosophy) and its nonsensicality (OK 74, where Russell asserts scepticism to be irrefutable), on Russell’s pragmatic acceptance of common knowledge as a condition for doing philosophy (OK 73, cf. 78), and Russell’s distinction of hard data (resistant to the acids of Cartesian doubt) from soft data (that dissolve). ‘My method’, Wittgenstein replies, ‘is not to sunder the hard from the soft, but to see the hardness of the soft.’

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It may seem that these programmatic propositions cohere with philosophical endeavours of the Investigations, and hence that what Wittgenstein proposed in the Tractatus, he executed in the Investigations. For, to be sure, what he is doing in the Investigations is precisely clarifying thoughts, thoughts about language and representation (the Augustinian conception of language is deeply confused), about a connection between language and reality (in the relevant sense, there is none), about determinacy of sense (the idea was incoherent). There are no doctrines (theses) in the Investigations. And the book does elucidate a wide range of issues: the nature of linguistic meaning, the character of family-resemblance concepts, following a rule, the incoherence of the idea of a private language, and so forth. But this is far removed from what he had had in mind in the programmatic remarks of Tractatus 4.112. The logical clariﬁcation of thoughts envisaged there is the analysis of propositions into truthfunctional combinations of elementary propositions. It is the analysis of elementary propositions and the uncovering of their logical forms — a task not even begun in the Tractatus, but deferred for later investigations into the ‘application of logic’ (duly undertaken in ‘Some Remarks on Logical Form’ in 1929). And the ‘Klarwerden von Sätzen’ is supposed to show that apparently vague sentences are really, on analysis, determinate in sense. This is all dismissed by the later Wittgenstein as chimerical. The conception of analysis was ﬂawed. The idea of an elementary proposition consisting of simple names in concatention was incoherent. The idea that every proposition has a determinate sense, and that any indeterminacy is determinately indeterminate was a confusion. Hence it would be misleading to present the Tractatus programme for future philosophy as an anticipation of the Investigations conception (and practice) of philosophy. The conception of depth analysis that dominates the Tractatus is dismissed. Russellian analysis on the model of the Theory of Descriptions is reduced to the very modest proportions it merits (PI §§90f.). The term ‘analysis’ may perhaps be retained, but with quite different connotations. Now we can say that a proposition is ‘completely analysed’ when its grammar has been laid out completely clearly (BT 417).24 The proof of a mistaken analysis, in this sense, is that it leads to patent nonsense, i.e. to an expression that transgresses the grammar that corresponds to the given // normal // mode of application of the expression (MS 110 (Vol. VI), 23). The Investigations offers us philosophy without illusions. There is no promise of wonderful treasures to be won, only the promise of learning one’s way around. The magic has not vanished, for there is magic in the dispelling of the illusions of metaphysics. If past philosophy took us into the cave to show us golden jewelry inlaid with diamonds, rubies and emeralds, the task of philosophy grown to maturity is to take these false treasures into the cold light of day, and show that they are nothing but rusting iron and old stones (cf. CV 11). 24

This conception was later characterized by Strawson as ‘connective analysis’.

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In philosophy there cannot be progress in the sense in which there is in the empirical sciences, i.e. accumulation of knowledge and attainment of more powerful explanatory theories. But there is progress in so far as clearer distinctions are drawn, conceptual afﬁnities and differences are deﬁnitively identiﬁed, conceptual connections are rendered explicit, and confusions dissolved. However, the progress may appear greater than it is. A conceptual ﬁeld may be partially illuminated for one generation, only to be cast into shadow again. Innovations occur (e.g. the invention of the computer, or of functiontheoretic logic), and new scientiﬁc theories are introduced (e.g. quantum mechanics, relativity theory). These may cast long shadows over conceptual articulations previously clariﬁed, requiring old ground to be traversed afresh from a new angle (e.g. the need to clarify yet again the concept of mind in response to the temptation to conceive of the mind on a computational model). Unlike in the sciences, there may also be regress in philosophy. The sciences are hierarchical. They build upon antecedently acquired knowledge and conﬁrmed theory. Their ever-advancing theories are put to the test by experiment and into practice by resultant technologies. Philosophy, by contrast, is ‘ﬂat’. It yields no knowledge and has no applications. Its distinctions can be lost from sight. Methods of clariﬁcation may fall into disuse, and the skills they require may vanish. Conceptual confusions may be cured for one generation, but the virus may mutate and reappear in an even more virulent form.25 So a new cure must be found, appropriately adjusted to the mutation and host. The work of philosophy has no end (Z §447). The ground has to be ploughed over again and again. Knowledge can be transmitted from one generation to another. But understanding has to be achieved afresh by each generation.

25

So, for example, ‘internal representations’ that appeared in the late twentieth century are merely mutant sense-data, and ‘qualia’ are Wittgensteinian private objects in new guise.

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

XV Surveyability and surveyable representations 1. Surveyability The notion of surveyability is prominent in all Wittgenstein’s later philosophy. It occurs on the second page of Philosophical Remarks, is discussed at some length in MS 110 (Vol. VI) in connection with Frazer’s Golden Bough, and is part of the characterization of the method of philosophy in section 89 of The Big Typescript. It looms large in his philosophy of mathematics,1 where he argues that surveyability is an essential property of a proof; and it is implicit in his fragmentary remarks on ethics and aesthetics. It is bound up with the notion of a surveyable representation, which is said to be the hallmark of Wittgenstein’s method, signifying the form of account he gives (PI §122): A main source of our failure to understand is that we do not command a clear view [übersehen] of the use of our words. — Our grammar is lacking in this sort of perspicuity [Übersichtlichkeit]. A perspicuous representation [übersichtliche Darstellung] produces just that understanding that consists in ‘seeing connections’. Hence the importance of ﬁnding and inventing intermediate cases. The concept of a perspicuous representation is of fundamental signiﬁcance for us. It earmarks [bezeichnet] the form of account we give, the way we look at things. (Is this a ‘Weltanschauung’?) (PI §122; see Exg.)

What exactly is meant by ‘an overview’? Why is our grammar lacking in surveyability? What is a surveyable representation? Where do we ﬁnd examples of such representations in Wittgenstein’s work? What is an understanding that consists in seeing connections? Is the description of intermediate links part of the surveyable representation, or does it merely facilitate the understanding that the latter produces? What is meant by saying that this concept characterizes the way Wittgenstein looks at things, the form of account he gives? And why does he query whether adopting this form of representation is a ‘Weltanschauung’? These are the questions that must be addressed. Notoriously, there is no happy way of translating ‘Übersicht’ and its cognates into English. Wittgenstein himself had difﬁculties with the translation (see Exg. §92, 1.1(ii)), and in his lectures often used the term ‘synopsis’. His 1

This aspect of the notion will not be examined here.

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translators have not found a consistent solution to the problem. The translators of the Remarks use ‘bird’s eye view’ for ‘übersichtlich’ and ‘Übersichtlichkeit’ (PR 52). ‘Übersichtlichkeit’ is rendered as ‘perspicuity’ (PI §122), but also as ‘synoptic view’ (Z §464); ‘übersehbar’ is translated as ‘capable of being taken in’ (RFM 170), ‘übersehen’ is given as ‘command a clear view’ (PI §122), ‘Übersicht’ is rendered as ‘survey’ (Z §273) and ‘übersichtlich’ both as ‘surveyable’ (PI §92) and as ‘perspicuous’ (PI §122). These translations are not incorrect, but the multiplicity obscures the centrality of this unitary idea in Wittgenstein’s works. Having tried unsuccessfully in the ﬁrst edition of this Commentary to get the archaism ‘a surview’ adopted as a translation of ‘Übersicht’ (because of its patent association with the verb ‘to survey’ and its cognates), I shall here adopt the Americanism ‘an overview’ instead. I translate ‘übersichtliche Darstellung’ as ‘surveyable representation’. It would be partly true, but superﬁcial, to claim that the concept of an overview is a direct descendant of the Tractatus conception of ‘the correct logical point of view’ (TLP 4.1213). The partial truth lies in the similarities in the respective roles of the two ideas and in the visual metaphors they both invoke for attaining a ﬁrm grasp of the way our conceptual scheme (the logical syntax of language (TLP) or grammar (PI)) hangs together. The superﬁciality lies in the fact that pointing out the similarity fails to draw attention to the ramifying differences. There are manifold connections between the concept of an overview and other concerns in Wittgenstein’s later reﬂections which are missing from the earlier notion. Moreover, profound methodological changes have occurred between the Tractatus and the Investigations. Accordingly, both the methods for attaining an overview and what comes into view when one attains one are importantly different from the conception of a ‘correct logical point of view’ of the Tractatus, which was linked to the idea of an ideal notation, to a distorted conception of formal and material concepts, to a misconceived idea of analysis, a mistaken conception of depth grammar (the logical syntax of language) as hidden beneath the surface of conventional grammar, and to the apparatus of atomism. It is noteworthy that at the end of 1931, Wittgenstein, in a letter to Schlick (below p. 327), characterized the main difference between the Tractatus and his new philosophy in terms of the contrast between analysis (as previously conceived) and tabulating the grammatical use of words in a surveyable representation. The visual metaphors that characterize both conceptions are natural, given that the passionate pursuit of clarity characterizes the whole of Wittgenstein’s philosophical endeavour: ‘For me’, he wrote in 1930, ‘clarity, perspicuity, are ends in themselves’ (CV 7). The unclarities against which he had struggled in the Tractatus were those generated by the outward forms of language which, he thought, conceal its true logical forms and lead us to ask meaningless questions, to assert nonsensical sentences (TLP 4.002f.), and to misunderstand the logic of our language (TLP, Preface). In his later philosophy Wittgenstein struggles against ‘conceptual’ or ‘grammatical’ unclarities ((PI p. 206/175;

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BT 409) and ‘conceptual confusion’ (PI p. 232/197). The goal of philosophy, he wrote, is ‘transparency of arguments’ (BT 414) and the ‘clariﬁcation of the use of language’ (BT 422) in order to dissolve philosophical problems. The quest for clarity invites visual metaphors of seeing things clearly, obtaining a clear view, of transparency and perspicuity. Wittgenstein duly capitalized on this. In the Tractatus, philosophy was said to strive for a correct logical point of view (TLP 4.1213). When one achieves this, one will be able to see the forms and limits of thought, and apprehend what can and cannot be said. Then one will see the world aright (TLP 6.54). One attains a correct logical point of view in respect of any domain of thought and language by logical analysis that delves beneath the surface of language in order to disclose the logical forms of things which are reﬂected in, and shown by, logical syntax. This sublime investigation will yield not only insights into the essential forms of thought and language, but above all insights into the essence of the world. In the Investigations, philosophy has lost its nimbus. It has abandoned its pretensions to the sublime, although it retains its depth — since the illusions it exposes are as deeply rooted in us as the forms of our language from which they typically spring. It aims to attain, or to enable its readers to attain, an overview of our use of certain words. The point of attaining an overview is to resolve philosophical problems. What one can do, when one has an overview, is survey the linguistic environs of a problematic expression. One can ‘see’ (take in) the use of the problematic concept, its manifold grammatical connections with related concepts, as well as the differences between it and concepts with which it is liable to be confounded. The transition from the Tractatus to the later philosophy involves replacing the Tractatus geological metaphor for what comes into view by a topographical one. According to the Tractatus, one sees the deep structures of language that are hidden beneath the surface syntax of ordinary language and which need to be dug out by analysis. Less metaphorically, one apprehends correctly the relevant segments of the hidden logical syntax of language, has an explicit understanding of logical form, and so too of the limits of language. According to the Investigations, one sees the multitude of familiar paths leading off in every direction from a given expression (PI §525). Less metaphorically, one apprehends the use of an expression, is reminded of its combinatorial possibilities, its entailments and incompatibilities, the presuppositions of its use, the similarities and differences between its use and that of other, confusingly similar expressions. The achievement of an overview, like the achievement of a correct logical point of view, betokens the acquisition of a set of abilities. When one has an overview of a conceptual ﬁeld, one knows one’s way around. Knowing one’s way around a conceptual ﬁeld consists in the ability to specify connections, exclusions, analogies and disanalogies that make it possible to dissolve and resolve philosophical problems. An overview is something one has when one can see across a landscape from on high — or across a wide ﬁeld of concepts and their connections. When one has an overview, one can say how the things that are in view stand

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in relation to one another. That looks like a river, but it is actually a railway track; this seems to be a bridge, but actually it is just a fallen tree that will not take one across; what look like clouds on the horizon are actually mountains, etc. That which one has in view must be something that is, in principle, surveyable (‘übersehbar’), otherwise one could not attain an overview (‘Übersicht’) of it. Of course, it may be difﬁcult to get the lie of the land in view (one may have to traverse dangerous crevasses and scale rock faces to reach the summit from which to see the landscape). Our grammar is deﬁcient in surveyability (‘Übersichtlichkeit’ (PI §122)), and all manner of misleading features make it ﬁercely difﬁcult to discern how things are in the normative domain of grammar. When one has attained an overview, when one has a clear grasp of the terrain, one can represent what is then in view in the form of a map — or, less metaphorically, in the form of a description of the salient grammatical features of the problematic expression or segment of language.2 However, Wittgenstein’s conception of surveyability has associations not brought out by emphasizing its Tractatus ancestry. He drew attention to the connection between surveyability and (i)

(ii)

(iii)

(iv)

(v)

the importance of seeing intermediate links (and, in philosophy, of inventing notional language-games to make such connections), that sharpen our eyes to formal relations between phenomena; the signiﬁcance of seeing aspects of, and formal relations between, phenomena, for it is such insights that dissolve certain kinds of problems, including philosophical ones; the repudiation of explanatory hypotheses in philosophy, for an overview of a ﬁeld of concepts clariﬁes conceptual relations without hypothesizing anything — there is no room for hypotheses in the realm of grammar (in so far as it contributes to philosophical elucidation); scientiﬁc creativity, and the role of models in science; for the notion of an overview was emphasized, by thinkers Wittgenstein admired, as crucial for the generation of fruitful analogies in science; the illuminating power of an overview for understanding in aesthetics, religion, ritual and mythology (or, more generally, perhaps, hermeneutics).

There are two complementary ways to try to present the signiﬁcance of the concept of an overview in Wittgenstein’s writings. One is historical; the other is to elaborate the connections which this concept has with the related notions just mentioned. 2

‘My aim’, Wittgenstein wrote for his pupils, ‘is to teach you the geography of a labyrinth, so that you know your way about it perfectly’ (MS 162b, 6v). The philosopher (in philosophy of mathematics) does not have to erect new buildings, or construct new bridges, but ‘to describe the geography as it now is’ (MS 127, 199). ‘The philosopher wants to master the geography of concepts’ (MS 137, 63a).

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2. Precursors: Hertz, Boltzmann, Ernst, Goethe, Spengler The historical route consists in bringing to light some of the inﬂuences upon Wittgenstein’s thought which contain seeds of the idea of surveyability and its importance. One need not claim that Wittgenstein’s conception was derived from these sources, only that these thinkers, whom we know Wittgenstein respected, moved along parallel tracks. What is important is that he thought of himself as advocating and practising a form of clariﬁcation which, as he understood them, these thinkers too advocated and practised. Wittgenstein acknowledged the inﬂuence of two great philosophically minded scientists — Hertz and Boltzmann. He much admired Hertz’s introduction to The Principles of Mechanics, and viewed the famous passage from the ‘Introduction’ as an exemplary statement of philosophical method (and was tempted to use part of it as the motto for the Investigations (see ‘The Motto’ Exg.). Hertz saw that some of the deepest and seemingly intractable problems in physics are to be resolved, not by scientiﬁc explanation and hypothesis, but by clariﬁcation. In such cases, what is needed is not fresh information about the phenomenon or sharper deﬁnitions of the theoretical concepts, but a clearer understanding of existing information and deﬁnitions. In particular, what is necessary is the removal of contradictions between known relations and the elucidation of conceptual connections — in short, an overview of the conceptual relationships. Then ‘our minds, no longer vexed, will cease to ask illegitimate questions’. In the same vein, Wittgenstein wrote: ‘As I do philosophy, its entire task consists in expressing myself in such a way that certain troubles // problems // disappear. ((Hertz.))’ (BT 421). Less well known, but no less important, are some of Boltzmann’s remarks. In his youth Wittgenstein had wished to study under Boltzmann, although, as a result of Boltzmann’s suicide in 1906, he was unable to do so. None the less, in 1931 he cited Boltzmann as a seminal inﬂuence upon his thought (MS 154, 16r). He was alluding to Boltzmann’s writings, in particular to his discussions of surveyability, model-building and analogy. Boltzmann explicitly relates models to surveyability: [T]here is a need for making the utmost use of what powers of perception we possess, and since the eye allows us to take in the greatest store of facts at once (signiﬁcantly enough we say ‘survey’), this gives rise to the need to represent the results of calculations and that not only for the imagination but visibly for the eye and palpably for the hand, with cardboard and plaster.3

3

‘On the Methods of Theoretical Physics’, in Ludwig Boltzmann: Theoretical Physics and Philosophical Problems, ed. B. McGuinness, tr. P. Foulkes (Reidel, Dordrecht, 1974), pp. 5f. (Subsequent page references to this and other papers by Boltzmann are to this volume.)

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He then elaborates a radical account of models in science. The beginnings of modern science conceived of achievement in terms of constructing explanatory hypotheses. But just when nineteenth-century science reached its apogee with Darwin’s theory of evolution, physics, under the guidance of Kirchhoff, reversed its steps. It cannot be the task of theory to see through the mechanisms of nature, but only to set up the simplest possible differential equations to enable accurate calculation and prediction. Indeed, under Hertz’s guidance, the attack on explanatory hypotheses went to extremes: hypotheses are mere colourful wrappings for bare equations. But others, especially fond of the ‘colourful wrappings’, while renouncing them as hypotheses, insisted on their importance as models and analogies (Faraday, Maxwell, Thomson). The mechanical models Maxwell presented in expounding his theories of electricity are not hypotheses, but analogies.4 The discovery of the great formulae was a consequence of the ingenuity and insight in creating fruitful mechanical analogies, a point missed by Hertz. Helmholtz’s discussions of the mechanical analogies of the second law of thermodynamics, Boltzmann wrote, . . . were more in tune with the spirit of science than the old hypotheses, besides being more convenient for the scientist himself. For the old hypotheses could be upheld only so long as everything went well; but now the occasional lack of agreement was no longer harmful, for one cannot reproach a mere analogy for being lame in some respects . . . In the end, philosophy generalized Maxwell’s ideas to the point of maintaining that knowledge itself is nothing else than the ﬁnding of analogies.5

The analogical approach to science, in Boltzmann’s view, compensates for abandonment of complete congruence with nature by revealing more striking points of similarity. No doubt the future belongs to this new method, he concludes, although it would be wrong to abandon the old method completely. Wittgenstein, moving along parallel tracks, held that the real achievement of a Copernicus or a Darwin is not so much the discovery of a true theory, but the disclosing of a fruitful new aspect (MS 112 (Vol. VIII), 117v).6 This suggests an afﬁnity with Boltzmann’s remarks on the importance of analogical thought. Maxwell’s analogical models were not mere colourful wrappings, but the creation of a fruitful analogy which would make possible a uniﬁed ‘overview’ of a domain of observation. Scientiﬁc creativity often consists in 4

In MS 111 ( Vol. VI), 120, Wittgenstein observed that one must not project features of one’s chosen form of representation on to the objects represented, or think that the things represented must have certain features which are in fact features of the mode of representation. This remark, he added, is actually what Boltzmann said about the status of mechanical models in the theory of electricity. (Cf. PLP 77, which, to illustrate the same point, cites Boltzmann’s methods of describing a model for Maxwell’s equations.) 5 ‘On the Methods of Theoretical Physics’, p. 11. 6 This arguably underestimates the importance and power of the explanatory theories they discovered.

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the choice or invention of a new form of representation which can fruitfully unify the facts. No less striking are passages, often echoing Hertz, in which Boltzmann warns against illegitimate (and commonly unnoticed) extensions of concepts from one domain to another.7 He stresses that the simplest pre-conditions of experience and laws of thought can only be described, and that this description will dissolve apparent contradictions involved in philosophical puzzlement, since it will show the nonsensicality of the questions.8 He also emphasizes the importance of ‘The overview of the whole, required for any mental activity aiming at discovering something essentially new or even just essentially new combinations of old ideas’.9 For an overview of the whole makes it possible to see how the different components of the whole hang together, and that in turn may produce new knowledge that takes the form of realization. Boltzmann’s endorsement is coupled with a warning: ‘Only half of our experience is even experience, as Goethe says. The more general the overview one can win, the more surprising the facts one can discover but the more easily too one can fall into error.’10 Finally, Boltzmann recurrently emphasizes that the ‘great problems’ (why anything exists, why the law of cause and effect holds, what might be the true cause for the world to run as it does, etc.) are illusory. It is not the task of science to give ultimate explanations, but merely to construct fruitful models. Nor is it part of its role to ‘solve the question as to the nature of matter, mass and force’, but rather, as Hertz had suggested, to dissolve it. My present theory is totally different from the view that certain questions fall outside the boundaries of human cognition. For according to that latter theory that is a defect or imperfection of man’s cognitive capacity, whereas I regard the existence of these questions and problems themselves as an illusion. On superﬁcial reﬂection it may of course be surprising that after recognition of the illusion the drive towards answering these questions does not cease . . . . . . Only very slowly and gradually will all these illusions recede and I regard it as the central task of philosophy to give a clear account of the inappropriateness of this overshooting the mark on the part of our thinking habits . . . If therefore philosophy were to succeed in creating a system such that in all cases mentioned it stood out clearly when a question is not justiﬁed so that the drive towards asking it would gradually die away, we should at one stroke have resolved the most obscure riddles and philosophy would become worthy of the name of queen of the sciences.11

7 8 9 10 11

‘On the Question of the Objective Existence of Processes in Inanimate Nature’, p. 67. Ibid., p. 75. ‘On the Development of the Methods of Theoretical Physics in Recent Times’, p. 77. Ibid., p. 96. ‘On Statistical Mechanics’, p. 167.

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One could look upon these remarks as the expression of an insight analogous to both the programme of the Tractatus12 and, differently applied, that of the Investigations. Paul Ernst was another source of inspiration. Wittgenstein expressed regret at not having acknowledged his inﬂuence in the Preface to the Tractatus. The essay of Ernst which impressed him was the Nachwort to Grimm’s Kinderund Hausmärchen (1910).13 What are the main points in Ernst which parallel Wittgenstein’s reﬂections? First, Ernst emphasizes that myths, folk-tales and fairy-tales are a repository of mankind’s moral beliefs. They express a world-picture and a fundamental belief in a moral world-order. They give a picture of the moral law, not by moralizing tales, but by poetic imagination, exaggeration, impossibilities and repetitions. It is a mistake to examine a folk-tale for ‘internal explanation’, i.e. for causal chains and intelligible motivation. For that is not what a folk-tale, consciously or unconsciously, is trying to achieve. Secondly, and consequently, Ernst sharply distinguishes the nature of understanding myth from scientiﬁc or historical explanation, and what is expressed by myth from what is aimed at by scientiﬁc understanding. To approach a myth or fairy-tale with questions such as ‘Did it really happen?’, ‘How could this be?’, is nonsensical — a misplaced rationalism. Science looks for explanations of facts, for a theory. But understanding of folk-tales is not to be sought thus. Poetic imagery and symbolism are part of the natural medium of folk-tale (it is natural to represent the common conception of the relation of body to soul as horse to rider, or servant to master). Historical explanation has a role in understanding folk-tales, not for purposes of historical understanding, but rather in so far as it illuminates an aesthetic understanding.

12

The impact of Boltzmann’s writings on the Tractatus is striking, especially, but not only, on the discussion of natural science in 6.3ff. Thus compare 6.342 with Ludwig Boltzmann, p. 106, 6.3611(a) with p. 103, 6.371 with p. 104, the network analogy with pp. 118f., and 5.1361(b) (which should be translated ‘Superstition is the belief in the causal nexus’ (see Ludwig Wittgenstein: Letters to C. K. Ogden, ed. G. H. von Wright (Blackwell, Oxford, 1973), p. 31) with p. 139. 13 Rhees reports that Wittgenstein said that he took the phrase, ‘mythology in our language’ from this essay. I have been unable to ﬁnd it there, although §93 of The Big Typescript seems to attribute it to him (the last section of the chapter ‘Philosophie’ is entitled ‘Die Mythologie in den Formen unserer Sprache ((Paul Ernst))’. Nietzsche, however, used the expression in The Wanderer and his Shadow, §11: ‘Through words and concepts we are now continually tempted to think of things as being simpler than they are, as separated from one another, as indivisible, each existing as and for itself. There is a philosophical mythology concealed in language . . .’. Whether or not Wittgenstein read this work, he thought of the idea that language, in some sense, contains a mythology as derived from Ernst. Ernst’s phrase ‘missverstandene Tendenz der Sprache’, p. 273 (as well as ‘eine spätere Zeit die Sprachlogik der Vergangenheit nicht mehr verstand’, p. 308) is the source of the phrase (and underlying conception) ‘Missverständnis der Logik unserer Sprache’ (TLP, Preface) and ‘unsere Sprachlogik nicht verstehen’ (TLP 4.003). In MS 110 (Vol. VI), 184, Wittgenstein remarks that when his book is published, he must acknowledge his debt to Ernst for this phrase, which he should have acknowledged in the Tractatus.

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Thirdly, Ernst emphasizes that now that science (cognition) is no longer one with religion and poetry, the creative myth-making powers of mankind are split up. But science itself creates, for itself, a great mythology. Theories of history, Darwinism, the Kant–Laplace theory, laws of gravitation, etc., all contain grandiose myths. Where do we ﬁnd the echoes of these remarks in Wittgenstein? In the Tractatus, perhaps in the remarks on ethics, aesthetics and religion, as something that can be shown but not said. Also, no doubt, in the analogy between misunderstanding the logic of language in myth and folk-tale (where inanimate objects have souls, men have extraordinary powers of bodily transformation, etc.) and philosophical misunderstandings of the logic of language. But it is striking that Ernst’s remarks resonate powerfully in Wittgenstein’s later writings, particularly in the ﬁrst set of ‘Remarks on Frazer’s “Golden Bough” ’ (derived from MS 110 (Vol. VI)), which is the source of the main remarks on surveyability, and in the Lectures on Aesthetics. Frazer’s approach to ritual and magic is not unlike the rationalist approach to myth and folk-tale. Wittgenstein’s reaction to Frazer is akin to Ernst’s brief castigation of rationalist interpretations of myth. Wittgenstein’s repudiation of explanation resembles Ernst’s, and his search for understanding by means of an overview resembles Ernst’s conception of poetic understanding. Wittgenstein’s adamant insistence upon the autonomy of the aesthetic bears a kinship with Ernst’s cast of mind. His pungent remark that Freud has not given an explanation of ancient myths (e.g. Oedipus), but propounded a new myth (LA 51), and his (highly questionable) intimation that Darwinism was accepted, like Freudian psychoanalysis, not as a theory resting on slender evidence but because of the charm of its unity (LA 26), seem in agreement with Ernst on the myth-making of science. A quite different connection, which Wittgenstein discussed with Waismann (VoW 311), is with Goethe’s morphological method as manifest in his conception of the Primal Plant. Goethe’s original inspiration for his botanical researches appears to have been a mixture of geneticism and analogical insight that might be put to work for purposes of comparative morphology. One can see the intermingling of the two in his remarks in Italian Journey;14 on 27 September 1786 he wrote: Here, where I am confronted with a great variety of plants my hypothesis that it might be possible to derive all plant forms from one original plant becomes clear to me and more exciting. Only when we have accepted this idea will it be possible to determine genera and species exactly.

On 17 April 1787 he wrote in a striking passage:

14

Goethe, Italian Journey, tr. W. H. Auden and Elizabeth Mayer (Penguin, Harmondsworth, 1970).

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Among this multitude [of plants] might I not discover the Primal Plant? There certainly must be one. Otherwise, how could I recognize that this or that form was a plant if all were not built upon the same basic model?

In a letter to Herder a month later (17 May 1787) he wrote: The Primal Plant is going to be the strangest creature in the world, which Nature herself shall envy me. With this model and the key to it, it will be possible to go on forever inventing plants and know their existence is logical; that is to say, if they do not actually exist, they could, for they are not the shadowy phantoms of a vain imagination, but possess an inner necessity and truth. The same law will be applicable to all other living organisms. [italics added]

Illumination (or the dawning of an illusion) came on 31 July 1787: While walking in the Public Gardens of Palermo, it came to me in a ﬂash that in the organ of the plant which we are accustomed to call the leaf lies the true Proteus who can hide or reveal himself in all vegetal forms. From ﬁrst to last, the plant is nothing but leaf, which is so inseparable from the future germ that one cannot think of one without the other.

Note that two elements are a source of confusion: namely, (i) the suggestion that only a hidden unity could justify the application of a single term to diverse phenomena, and (ii) that the unity must be genetic and developmental. However, Goethe also came to think that the source of unity in diversity may be analogy, a strand in his thought which Wittgenstein exaggerated. Goethe expressed this in his criticism of Linnaeus, who, in his view, made too much of superﬁcial dissimilarities: For it is here that we hope the genius of the analogy may stand by us, as a guardian angel, so that we may not fail to recognize in a single doubtful case a truth which has stood the test in many other instances, but may instead pay due respect to the law, even when it seeks to elude us in the phenomenal world.15

Goethe’s conception of the principle of unity as determined by a Typus or Urbild is not (or not only — he seems to have vacillated) genetic or developmental, but (also) ideal. This betokens a Platonist strand in Goethe’s reﬂections, but Wittgenstein saw it as having a closer afﬁnity with his own conception of a surveyable representation — a way of organizing data, a principle or form for description and classiﬁcation. The phrasing in the letter to Herder may indeed have struck Wittgenstein as especially interesting, since in effect, it seemed, the ‘model’ of the Primal Plant was designed, as it were, to 15

Goethe, Die Schriften zur Naturwissenschaft, I, 10, p. 393, quoted and tr. H. B. Nisbet, Goethe and the Scientiﬁc Tradition (Institute of Germanic Studies, University of London, 1972), p. 15.

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provide the ‘logical space’ for all possible plants. Hence Schiller’s perceptive response to Goethe’s explanation of the metamorphosis of plants: ‘That is no experience, that is an idea.’16 Goethe gave his ideas poetic expression in ‘Die Metamorphose der Pﬂanzen’, which opens thus; Dich verwirret, Geliebte, die tausendf ältige Mischung Dieses Blumengewühls über dem Garten umher; Viele Namen hörest du an, und immer verdränget Mit barbarischem Klang einer den andern im Ohr. Alle Gestalten sind ähnlich, und keine gleichet der andern; Und so deutet das Chor auf ein geheimes Gesetz, Auf ein heiliges Rätsel. (You are confused, beloved, by the thousandfold mingled multitude of ﬂowers all over the garden. You listen to their many names which are for ever, one after another, ringing outlandishly in your ears. All their shapes are similar, yet none is the same as the next; and thus the whole chorus of them suggests a secret law, a sacred riddle.)17

Spengler, whom Wittgenstein cited as an inﬂuence upon his thought (see Exg. §122), viewed himself as a follower of Goethe, acknowledging that the philosophy of his book is indebted to Goethe’s. The subtitle of The Decline of the West was An Outline of a Morphology of World History. Spengler called for a ‘Copernican revolution’ in the way we view history that would abandon the conception of linearity and undermine the traditional trichotomy of ancient, medieval and modern history. In its place he wished to place a comparative morphology of cultures that would study their characteristic life-cycles and investigate their speciﬁc forms of life and thought. The life-cycle of a culture is, according to Spengler, comparable to that of a plant or an animal, with characteristic phases of childhood, youth, maturity and age (also characterized as spring, summer, autumn and winter). Spengler compared his morphological method in world history with Goethe’s morphological method in natural science. What both were seeking, he wrote, were the morphologically necessary interconnections, ‘a physiognomic that is precise, clear and sure of itself and its limits’.18 The historian with ‘physiognomic tact’ will be able to discern the qualitative changes in a culture that betoken the various processes of ageing. Waismann, writing under Wittgenstein’s guidance, compares the method of philosophical clariﬁcation, of dissolution of puzzlement by juxtaposition, analogy and disanalogy, ﬁrst with Boltzmann’s remarks on models, and then with Goethe’s essay Metamorphosis of Plants (PLP 71–81). He denies that the 16

Schiller’s remark is quoted by Wittgenstein in MS 110 (Vol. VI), 256, in the paragraph which precedes his quotation from ‘Die Metamorphose der Pﬂanzen’. See also Exg. §97, 2.1(iv). 17 Prose translation by D. Luke, Goethe: Selected Verse (Penguin, Harmondsworth, 1964), pp. 147f. 18 Spengler, Decline of the West, tr. C. F. Atkinson (Allen and Unwin, London, 1932), vol. i, p. 105.

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conception of the Primal Plant is a proto-Darwinian developmental hypothesis. ‘Goethe’s aphorism “All the organs of plants are leaves transformed” offers us a plan in which we may group the organs of plants according to their similarities as if around some natural centre’ (PLP 81; cf. VoW 311). The idea of representing the various organs of plants as different forms of a leaf solves the problem of a surveyable representation (PLP 81): we see the original form of the leaf changing into similar and cognate forms — into the leaves of the calyx, of the petals, into organs that are half-petals, half-stamens, etc. It is, I think, doubtful whether Goethe’s conception was that liberated from geneticism. However, Wittgenstein seems to have seen in it a precursor of his new methods in philosophy, and to have overlooked the differences. Comparison of our language (or parts of it) with invented calculi, and with language-games, he insisted, serves a similar function, i.e. to apprehend the distinctive features of our language. The point is not to explain on the model of science, but to clarify. This was Wittgenstein’s view in the early 1930s.19 He thought that there was an analogy between Goethe’s proposed methodology in biology and his own method of juxtaposing artiﬁcial, invented calculi with fragments of our language to dissolve philosophical problems. The realization that one form of representation can replace another, he had initially argued in the early 1930s, dissolves puzzlement by clarifying what is and what is not essential. It had brieﬂy seemed to him that a phenomenological language could replace our ordinary physicalist language, and that a language without a ﬁrst-person pronoun could replace our pronominal language (WWK 49; AWL 21f.). He subsequently came to think that what was at stake was not replacement but merely juxtaposition — which is the point Waismann stresses (residues of this conception are evident in Investigations §§130–3 (see Exg.)). In The Big Typescript, Wittgenstein observed that the rules of use of our language and their surveyable representation achieve the same as one often tries to achieve by constructing a phenomenological language. Whenever we realize that such-and-such a mode of representation can be translated into another, we take a step towards this goal (BT 437). It is debatable, however, whether the analogy with Goethe’s conception of the Primal Plant was all that good, and it is perhaps no coincidence that it is hardly mentioned after the early 1930s (but see MS 134, 154; RPP I, §950). It is questionable whether the leaf, chosen by Goethe as a form of representation for botanical typology (which proved theoretically fruitless), or the hydrodynamic model, chosen as a form of representation for electricity theory (which proved immensely fruitful), really are akin to the use of invented calculi for the purpose of dissolving philosophical perplexity (let alone to the use of the simpliﬁed language-games that replaced them when that method was abandoned). Among other things, the former aim at novel forms of classiﬁcation for scientiﬁc purposes. It is indeed fruitful to view electricity in the guise 19

This was the period when Waismann was in close contact with him, hence the prominence of these ideas in PLP.

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of ﬂow, to think of voltage as akin to pressure, amperage as akin to current, and electrical resistance as akin to hydrodynamic resistance. The upshot is a powerful predictive and explanatory scientiﬁc theory. But philosophical insight has no such theoretical, explanatory or predictive purposes. We must distinguish, as indeed Wittgenstein did in his discussion of Frazer, between (i) developmental hypotheses; (ii) organizing models or prototypes for the production of fruitful empirical theories or typologies; and (iii) an arrangement of the data that we are studying in such a manner as will enable us to survey it, to see analogies and connecting links (which can also be helpful in anthropology). ‘And so the chorus points to a secret law’ [is what] one feels like saying to Frazer’s collection of facts. I can express // present // this law, this idea, in a developmental hypothesis, or again, on analogy with the schema of a plant, by the schema of a religious ceremony, but also by the arrangement of the factual matter alone, in a ‘surveyable’ representation.20 (MS 110 (Vol. IV), 257; TS 211, 321)

Here we are offered three possibilities, and it is primarily the third which is akin to the morphological method in philosophy — where our ‘data’ are the familiar uses of words. This in no way diminishes the importance of the relation between the need for an ‘overview’ in science and anthropology and the analogous need in philosophy. In both cases the signiﬁcance of analogical insight is emphasized. But in the case of science the upshot is novel explanatory and predictive theories, in anthropology the understanding of ritual phenomena, and in philosophy an overview of grammar that dissolves puzzlements. Nevertheless, there is a connection between Wittgenstein’s method of clariﬁcation of conceptual structures and Goethe’s use of the schema of the leaf. Although Wittgenstein was not concerned with providing a typology for an empirical science, he was concerned with using examples as centres of variation around which we can group the grammatical data in a surveyable representation (MS 150, 6; MS 152, 17; MS 115 (Vol. X1), 221). This, at any rate, is analogous to what Goethe was suggesting with respect to the leaf, which (at least as Wittgenstein understood him) he viewed as a centre of variation around which to group the various organs of the plant. According to Wittgenstein, in our conceptual investigations, we often need to abandon the traditional quest for displaying the essence of a thing by means of an analytic deﬁnition. Rather, what we should do is to present judiciously chosen examples as centres of variation around which to group the multifaceted use of the problematic concept.21 The examples selected as centres of variation could be 20

W. quotes the same line, ‘Und so deutet das Chor auf ein geheimes Gesetz’, in MS 156(a), 49, and comments on it — it is not a law that we perceive but something that might be called the presentiment or idea of a law. 21 MS 115 cites the case of clarifying the nature of reading to exemplify what he has in mind; cf. PI §§156–71.

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said to be poles of a description, not the ground ﬂoor of a theory (cf. RPP I, §633). Hence prima facie counter-examples need not refute the account (as Plato constantly supposed in his essentialist quest) but may merely enrich it. Of course, the purpose of the exercise is quite different from Goethe’s in botany. One further point: Wittgenstein stresses that what looks like a hypothetical link or developmental hypothesis (and was thus understood, for example, by Frazer) may be no more than a way of presenting similarities and analogies, to sharpen our eye to a formal connection (analogously to noting the ‘generation’ of an ellipse from a circle). An appropriate arrangement of some of Frazer’s data would, Wittgenstein intimates, do far more to illuminate certain aspects of the phenomena that puzzled Frazer than his dubious developmental hypotheses. They would not have been ‘scientiﬁcally’ explained, but they would have been rendered intelligible as phenomena of human life — as forms of ritual, symbolic, expressive behaviour characteristic of mankind. To be sure, sharpening our eye to a formal connection is a crucial part of Wittgenstein’s methods, especially prominent in devising imaginary language-games. Thus far, Wittgenstein’s precursors and his responses to them. His remark ‘The concept of a surveyable representation is of fundamental signiﬁcance for us’ belongs to a certain cultural tradition, of which he was acutely aware. Moreover, he also associated it with his contemporaries Freud, Spengler and Loos (see Exg. §122 1.1(vi)), and wondered whether the quest for this particular form of understanding, both within and outside philosophy, was not akin to a Weltanschauung, a way of looking at things, characteristic of leading intellectuals of his times. In this he was surely mistaken. Such forms of elucidation did not prove to be the hallmark of twentieth-century thought, which, on the contrary, veered towards the misguided belief that all genuine questions are to be answered by scientiﬁc methods. Furthermore, neither Spengler nor Freud would have accepted Wittgenstein’s interpretation of their work. Indeed, Wittgenstein himself criticized these two for not seeing things in the right light — Freud for not seeing that the unconscious was not an empirical discovery but the introduction of a new form of description, and Spengler for not realizing that he had not discovered laws of history but only introduced an illuminating form of description.

3. The morphological method and the difﬁculty of surveying grammar It is evident that the ideas of clariﬁcation by description, rather than by explanation (conceived on the model of the sciences), and of elucidation by means of an overview of the data, rather than by hypothesis (as in the hypotheticodeductive model of science), are pivotal for Wittgenstein’s thought. This form of understanding has a place beyond the conﬁnes of philosophy. Surveyability, in understanding ritual and religious symbolism, plays a crucial role. Just because

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ritual is symbolic, a perspicuous representation of that ‘extremely developed gesture-language’ (GB 135) can resolve certain forms of perplexity where a developmental hypothesis cannot. Developmental hypotheses have their place, but sometimes that which is most deeply perplexing and disturbing cannot be resolved thus, although it is easy to be fooled into thinking it can. And this is important, for when genetic explanation overreaches itself, it can deprive us of an important bewilderment and rob us of the drive to understand precisely what it is that puzzles us (e.g. about the rule of succession at Nemi) or precisely what is the nature of our awe or horror (e.g. in the case of the Beltane ﬁre festival).22 The same point holds in the domain of aesthetics: genetic, causal explanations cannot touch the heart of many aesthetic problems. Indeed, they cheat us of our puzzlement, offering a causal explanation, where what we need is an overview that will make clear formal connections. The causal explanation distracts our attention from what is really puzzling us, since it invites further questions that take us farther and farther away from the aesthetic problem. In his Lectures on Aesthetics (LA 28), Wittgenstein emphasized that he was trying to effect a change in style of thought. It is plausible to take this as a pointer to the signiﬁcance of analogical elucidation, produced by a comprehensive survey of similarities and dissimilarities, and to the repudiation of the ubiquitous relevance of causal or genetic explanation. Explanation in aesthetics is commonly a matter of ‘certain comparisons — grouping together of certain cases’ (LA 29). Our main concern, however, is to understand the role of the idea of an overview of grammar, of concepts, uses of language or words in Wittgenstein’s philosophy, how such an overview is to be achieved, and how what then comes into view is to be described. In his lectures in 1946/7 he said: What I give is the morphology of the use of an expression. I show that it has kinds of use of which you had not dreamed. In philosophy one feels forced to look at a concept in a certain way. What I do is to suggest, or even invent, other ways of looking at it. What I do is to suggest possibilities of which you had not previously thought. You thought that there was one possibility, or only two at most. But I made you think of others. Furthermore I made you see that it was absurd to expect the concept to conform to those narrow possibilities. Thus your mental cramp is relieved, and you are able to look around the ﬁeld of the use of the expression and to describe the different kinds of uses of it.23

22

See F. Ciofﬁ, ‘Wittgenstein and the Fire-Festivals’, ‘Wittgenstein on Obscurantism’, and ‘Explanation and Self-Clariﬁcation in Frazer’, repr. in his Wittgenstein on Freud and Frazer (Cambridge University Press, Cambridge, 1998), pp. 80–106, 183 –205, 255– 63, and P. M. S. Hacker, ‘Wittgenstein on Frazer’s Golden Bough’, repr. in Wittgenstein: Connections and Controversies (Oxford University Press, Oxford, 2001), pp. 74–97. 23 N. Malcolm, Ludwig Wittgenstein: A Memoir, 2nd edn (Oxford University Press, Oxford, 1984), p. 43.

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It is striking that he should have used the term ‘morphology’ here, and it is not unreasonable to associate this with Goethe’s morphological method (as opposed to the method of hypotheses). Nor is it a coincidence that he quoted Goethe’s remark, ‘Man suche nichts hinter den Phänomenen; sie selbst sind die Lehre’ (‘Don’t look for anything behind the phenomena; they themselves are the doctrine’ (RPP I, §889)),24 for (rightly or wrongly) he saw an analogy between Goethe’s methodology in natural-historical investigation and his own methods of philosophico-grammatical investigation. Wittgenstein emphasized in his lectures that he was pointing out not merely philosophical confusions, ‘but the morphology of the confusion. . . . A philosophical puzzle comes when you have a limited morphology of the uses of language’ (LPP 47). When asked how to discover25 the morphology of language, he gave as an example the word ‘self ’ (he had just been discussing James’s confusions about ‘the Self ’). One ﬁrst (wrongly) asks what the word stands for — and here one immediately thinks of the body. When one realizes that the word ‘self ’ cannot stand for the body, one thinks that it must stand for something inside the body. But the mistake was to think that the word ‘self ’ stands for something in the way that ‘body’ stands for the body. If one considers substituting a signal for ‘I suffer’, one will see that ‘I’ does not stand for anything at all. ‘I try to make you see that “it isn’t like that”, but also that it needn’t be like that,’ he concluded (ibid.).26 The ‘morphological method’ here involves striving to attain an overview of the use of a word. One way of doing so is ﬁnding the appropriate analogies and comparisons in grammar that will enable us to see the use of a problematic expression aright, and undermining the wrong analogies and comparisons that are determined by the surface grammar alone and that distort our view. It is important, however, to note that the purpose of elaborating ‘possibilities’ other than those on the carpet is twofold. First, to relieve what Wittgenstein calls a ‘mental cramp’, i.e. a ﬁxation with a particular picture or form of words, or a form of dogmatism that consists in thinking that things (especially, but not only, things in grammar) must be thus-and-so. (So, for example, we are prone to think that because ‘he’ and ‘she’ stand for something or are referring expressions, ‘I’ must be too; or that because ‘He is in pain’ is a description, ‘I am in pain’ must be too; or that every real name must have a bearer, otherwise the sense of a sentence would depend on the facts.) Secondly, to enable one, now with a view freed from distortions, ‘to look around the ﬁeld of the use of the expression and to describe the different kinds of uses of it’ (ibid., emphasis added). 24

Goethe, Maximen und Reﬂexionen, ed. Max Hacker (Weimar, 1907), no. 575 (Spengler also quotes this remark in Decline of the West, vol. i, p. 156). 25 ‘Disclose’ would perhaps have been better. 26 This is patently a response to the disquietude that inclines us to say ‘But this isn’t how it is’ and also ‘Yet this is how it has to be!’ (cf. PI §112 and Exg.).

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It is important to understand why Wittgenstein stressed that he was concerned to elaborate possibilities. It is not to avoid having to describe our use of words — as if that would be dogmatism or would run the risk of asserting something that might be false. On the contrary, it is to enable us to give correct descriptions. (And if someone declares that he uses the word in question differently, then that does not matter; for we should simply ask him to explain how he does use it, and proceed from there (WWK 184) for the sake of the argument (AWL 97).) Nor is Wittgenstein’s talk of ‘other possibilities’ a matter of offering us different ‘ways of viewing things’ or ‘new visions’, which will ‘leave us free’ (as Waismann suggested27) and from among which we can take our choice. Rather, it is to offer us the correct way of viewing things, which is both faithful to the grammar of the problematic expressions under consideration and makes evident the philosophical nonsense in which we were enmeshed. It is not to abstain from deﬁnitively solving or dissolving philosophical problems — on the contrary, as he remarked, ‘If I am right, then philosophical problems must be completely solvable, by contrast with all others’ (BT 421). His deﬁnitive solutions are not given by showing us that grammar might be otherwise, but rather by reminding us that it is thus-and-so and showing us the consequences. To clarify his remarks about presenting ‘other possibilities,’ it is helpful to bring into view his targets. Wittgenstein was concerned with breaking the spell of pictures that hold us, and some of which had held him, in thrall (PI §115). With hindsight he thought that the confusions of the Tractatus were often rooted in his implicit belief at the time that logical grammar must be thus-and-so, that names must stand for simple objects (otherwise they might not reach right up to reality), that propositions must have the general form ‘This is how things stand’ (otherwise they would not be logical pictures), that any indeterminacy in surface grammar must be determinately indeterminate in depth grammar (otherwise logic could not be the depth grammar of all possible languages), and so on. As we have seen (‘Turning the examination around: the recantation of a metaphysician’, sects 4–5), this was the dogmatism of which he later accused himself. His subsequent recurrent stress on alternative possibilities is the negation of this dogmatism. First, the negation of ‘Things must be thus-and-so’ is ‘It is possible that things are not thus-and-so’. Names do not have to be simple, and they do not have to stand for simple objects. Indeed, the notions of absolute simplicity and complexity that were presupposed by the Tractatus were not coherent. ‘Harold Godwinson’ is a name, and it is not logically simple in one obvious sense of ‘simple’. It is perfectly possible for a genuine name (indeed, a simple name) to stand for a complex entity with multiple parts (as do, for example, proper names of cities, such as ‘London’ or ‘Paris’). So too, names do not have to 27

F. Waismann, ‘How I See Philosophy’, repr. in How I See Philosophy, ed. R. Harré (Macmillan, London, 1968). This late paper was written in opposition to Wittgenstein, in order to stake out Waismann’s own distinctive position.

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have a bearer — it is perfectly possible for a name to lose its bearer (if its bearer is destroyed or broken into pieces, like Nothung) or never to have had a bearer at all (like ‘Odysseus’ (Wittgenstein’s example), ‘Eldorado’ or ‘Utopia’) — and yet be a name for all that (cf. PI §§40–5 and Exg.). Similarly, propositions do not have to depict how things stand — ‘It is raining’ does not depict a distribution of objects in a network of logical relations (see ‘Turning the examination around: the recantation of a metaphysician’, sect. 3), nor do ‘2 + 2 = 4’, ‘Red is a colour’, ‘It is better to suffer, than to do, evil’, ‘I have a pain’, ‘I’m going to go’ — although all these are propositions. Secondly, very often what appeared to be necessary is not only not necessary, it is not even possible — i.e. it does not make sense.28 So not only is it possible that names do not stand for simple objects that are their meanings, but it is not even possible that names should do so. For there are no absolutely simple objects, and meanings are not entities in reality of any kind for which names might stand. Again, to take an example that is not concerned with his own early errors, Wittgenstein notes that the James–Lange ‘theory’ of emotion (roughly, that an emotion is a diffuse bodily sensation) is advanced with the thought ‘What else can it be?’ or ‘It’s got to be that way’ (LPP 45). Wittgenstein shows us not only that grammar need not function thus, i.e. that it was an illusion that things had to be thus-and-so, but also that this is not how grammar functions. It is not merely not necessary that emotions be bodily sensations — it is not even a possibility. Thirdly, where the ‘possibility’ in question is in grammar (as opposed to the possibility of alternative grammars), then, in a sense, it cannot be merely possible. Whatever is possible in grammar (as in mathematics) is, so to speak, a grammatical actuality. That is, it actually makes sense. Grammar determines what is logically possible, i.e. what it makes sense to say. It determines, as it were, logical space, the actual logical space within which we operate with our language — not, so to speak, a ‘possible’ logical space. Different grammatical possibilities can be envisaged; but they determine concepts different from ours.29 If, in our grammar, it is possible, for example, for a signiﬁcant name not to stand for an object, then it makes sense to speak of names which do not stand for an object — and this is part of the grammar of ‘name’. (It is not that it is possible that this be part of the grammar of ‘name’; rather, it is part of its grammar that it is possible for a name to lack a bearer.) And what makes sense is precisely what interests us in philosophy. 28

Of a mathematical example considered in the same lecture Wittgenstein said, ‘We seem in such cases to be nailed down to saying one of two absurd things and we cannot think of completely different possibilities’ (LPP 47). Here the apparent necessities, Platonism and formalism, to which we seem to be ‘nailed down’, are not only not necessary, they are not even possible. And the ‘possibility’ that Wittgenstein himself canvasses elsewhere concerning the status of mathematical propositions is argued to be a grammatical actuality, i.e. mathematical propositions are rules. 29 And that too is of interest, when it is necessary to make it clear that our grammar is not ‘true to the facts’, or ‘correct’, or the only possible grammar.

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Philosophical problems are not resolved by adducing new facts or discovering new truths. ‘We want to understand something that is already in plain view’ (PI §89) — the network of grammar with all its complex ramiﬁcations and connections, local and global similarities and dissimilarities, analogies and disanalogies. But the grammar of our language is lacking in surveyability (MS 108 (Vol. IV), 31; BT 417).30 This is one great source of philosophical problems (MS 115 (Vol. XI), 52). The uses of expressions cannot be taken in at a glance, and their surface grammar is deceptive. Form does not reﬂect use, and expressions with very different uses may share a common appearance in surface grammar, e.g. ‘I went’ and ‘I meant’, ‘to fear failure’ and ‘to fear Freddie’, ‘3 is greater than 2’ and ‘Jack is taller than Jill’. One may master the use of expressions without being able to survey that use (MS 130, 220).31 So one may talk perfectly correctly of thinking of something, or solving a problem, in a ﬂash, and speak rightly of the lightning speed of thought. But if asked how thought can be so fast, how problems can be solved in a ﬂash, one may be attracted to a completely misconceived picture, modeled upon misguided analogies (e.g. on analogy with executing physical activities swiftly). One may speak perfectly correctly of meaning someone or something by what one said, but have an altogether muddled conception of what meaning someone or something amounts to, a conception informed by the misleading surfacegrammatical analogy between meaning something and doing something. To attain an overview of a problematic expression, one must compare it to different expressions from those suggested by its surface grammar. (Something that looks like a jawbone, Wittgenstein suggests (perhaps with an allusion to Goethe on the intermaxillary), may have to be compared with a foot (MS 134, 126).) So, for example, saying that Jack is ill and meaning Jack Jones (not Jack Smith) must be compared not with doing two different things simultaneously, but with doing one thing and intending something by it. The verb ‘to mean’ looks like a verb of action such as ‘to say’ (a jawbone, as it were), but should be compared with the verb ‘to intend’ (a foot). Saying ‘Now I can go on’, when one suddenly understands, should be compared with a signal or a start of understanding — not with a report. Then it will become clear that understanding something in a ﬂash is not doing something at high speed, but the dawning of an ability. In trying to attain an overview, one should note not only similarities between the problematic expression and others, but also connections (a father passes on his name to his son even though his son does not resemble 30

Interestingly, his example of deﬁciency of surveyability here is that the rules for the logical connectives which he had given in the Tractatus do not exhaust their use. It was not evident (in the surface grammar) that logical relations can be determined not by truth-functional combinations of, but by the content of, elementary propositions, e.g. in the case of determinates of a determinable. So the TT line in the truth-table for ‘A is red & A is green’ must be excluded. 31 It is noteworthy that this contrast is different from the more questionable one between explicit and tacit knowledge or understanding, which was much invoked by philosophers and theoretical linguists in the 1970s.

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him at all). Hence the importance of ﬁnding or inventing intermediate links (PI §122) — for they make perspicuous formal connections (cf. GB 133). Describing the morphology of a particular expression which is giving us trouble has as its purpose the dissolution of confusion and bafﬂement. The description removes misunderstandings that stem from false analogies (e.g. between meaning something and doing something, or between thinking and speaking), from misguided questions (e.g. ‘In what relation does the mind stand to the body?’, ‘What do mathematical propositions describe?’), from failure to apprehend the normative status of grammatical propositions (e.g. that ‘Nothing can be red and green all over simultaneously’ is a norm of representation, not a description of a necessity in nature), and from misleading pictures embedded in language (e.g. the measurement of time, the possession of experience, introspecting (‘inwardly perceiving’) what is going on in one’s mind). Describing the morphology of the use of an expression and anatomizing the confusions that surround it are the complementary, interdependent, positive and negative aspects of philosophical clariﬁcation.

4. Surveyable representations The concept of a surveyable representation, Wittgenstein declared, is of fundamental signiﬁcance for him — it characterizes the way he looks at things (PI §122). This remark has occasioned controversy. What counts as a surveyable representation? Where does one ﬁnd such surveyable representations in Wittgenstein’s work? How is advancing a surveyable representation related to the aim of attaining an overview of segments of grammar in order to resolve philosophical difﬁculties? And what does he mean by his further query of whether this is a ‘Weltanschauung’? Despite Wittgenstein’s claim that this concept is of fundamental signiﬁcance for him (and for his way of doing philosophy), this phrase is rarely used in his work, and does not occur again in the Investigations. The remark originates in Wittgenstein’s reﬂections on Frazer’s Golden Bough (MS 110 (Vol. VI), 257). There, having quoted Goethe’s poem ‘Metamorphosis of Plants’, and having differentiated developmental hypotheses both from schemas and from arrangements of data in a surveyable representation, he remarks that the latter concept is of fundamental signiﬁcance for him, characterizing the form in which he presents things. This form of presenting things is, he suggests, a kind of ‘Weltanschauung’, which is perhaps typical of his times — and adds in parentheses ‘Spengler’. There can be no doubt that he is referring to the ‘morphological method’ of The Decline of the West, which he is invoking here in his criticisms of Frazer.32 32

It is also noteworthy that after these reﬂections, and after the discussion of the importance of intermediate links in sharpening our eye to formal connections, he mentions Goethe’s antipathy to laboratory experiments and to hypotheses (wrongly conceived) as being already falsiﬁcations of the truth, which can be observed freely in nature.

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And it seems that he associated the morphological method not only with his own work, but also with Freud (see Exg. §122, 1.1(vi)). This passage, more or less as it occurs in Investigations §122, was transcribed into The Big Typescript, where it is detached from reﬂections on Frazer and generalized. The section head within which it occurs is ‘the method of philosophy: the surveyable representation of grammatical // linguistic // facts. The goal: transparency of arguments. Justice (BT 414).’33 No indication is given as to what counts as a surveyable representation of grammatical facts, but it is perhaps signiﬁcant that the next remark is: A proposition is completely logically analyzed when its grammar is laid out completely clearly [vollkommen klargelegt]. It might be written down or spoken in any number of ways. Above all, our grammar is lacking in surveyability. (BT 417)

This remark, if it is to be read in association with the previous one, suggests that a surveyable representation lays out the grammar of an expression (a) completely clearly, and (b) such that it can be taken in or surveyed. This conjecture is borne out by a letter to Schlick dated 20 November 1931 (i.e. not long after writing the remarks on Frazer), apparently in response to a request from Schlick to give examples of simple names and elementary propositions. In it Wittgenstein remarks that with ‘very, very many’ of the formulations of the Tractatus he is no longer in agreement. His views have undergone fundamental transformation, but for the moment he can make only one observation, even though he is unsure whether it will help Schlick. Perhaps the main difference, he writes, between the conception advanced in the Tractatus and his current one is that he now realizes that the analysis of propositions does not turn on discovering hidden things, ‘but on tabulating, on the SURVEYABLE REPRESENTATION of, grammar, i.e. the grammatical use of words’ (‘sondern im Tabulieren, in der ÜBERSICHTLICHEN DARSTELLUNG, der Grammatik, d.h. des grammatischen Gebrauchs, der Wörter’). With this, he continues, everything dogmatic that he had said about objects, elementary propositions, etc. collapses. If one wants to understand the word ‘object’, for example, then one should look to see how it is actually used. This letter gives us revealing clues regarding what he had in mind and how he thought that his new methods contrasted with his old ones. It makes clear why he said that a perspicuous representation of grammar (the grammar of the expressions that are causing us difﬁculties in philosophy) is the hallmark of his new philosophy (conceptual topography, or the morphology of concepts) and also what he is contrasting it with (conceptual geology, or depth analysis). However, the matter is controversial, and it is appropriate that we examine other evidence too. 33

‘Gerechtigkeit’, i.e. doing justice to, and avoiding the distortion of, the grammatical facts.

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Trawling through Wittgenstein’s other writings for observations on what counts as a surveyable representation of grammar yields a meagre catch. In 1929/30 he gave as an example of a surveyable representation of a segment of grammar the colour octahedron. It presents the rules for the use of colourwords in a readily surveyable way. It ‘wears the rules of grammar on its face’ (PR 278; cf. 75); it ‘is really a part of grammar . . .’, he said in his lectures, ‘It tells us what we can do; we can speak of a greenish blue but not of a greenish red’ (LWL 8; cf. VoW 135). In a dictation to Waismann, he implied that the T/F notation of the Tractatus, being readily surveyable, provided a perspicuous representation of rules of inference (VoW 129), and suggested that a model of a cube can be used in geometry as a perspicuous representation of the geometry of a cube (the grammar of ‘cube’). Barely anywhere else does he unequivocally characterize anything as being a surveyable representation. The colour octahedron is evidently an exception, inasmuch as it is a non-linguistic symbolic expression of a set of rules in a visually surveyable form (another exception is perhaps the square of opposition in logic). But there is, by and large, no aerial photography in grammar. It is clear that not anything that helps one to attain an overview is a surveyable representation of the grammar of an expression. It is true that he observes (surely correctly) that a good expression or good simile enables one to get an instantaneous overview (augenblickliche Übersicht) of things (MS 112 (Vol. VIII), 112r). But comparing words to tools, or comparing the contrast between the appearance of words and their uses to that between handles of levers and the functions of the levers (PI §§11f.), cannot be said to represent (or to present) the grammar of the word ‘word’. Comparing the use of a sentence with a move in a game (PI §49) is illuminating, and it may for someone be, as it were, a ‘redeeming word’ (erlösende Wort) which enables them to get an instantaneous overview of an essential feature of the grammar of ‘sentence’. But it cannot be said to represent the grammar of the word ‘sentence’ in a surveyable representation — and Wittgenstein nowhere suggests that it does. Putting the rules of draughts alongside the rules of chess may shed light on the latter by way of both similarities and differences, but the rules of draughts are not a surveyable representation of the rules of chess (it is not as if one can read the rules of chess off the rules of draughts!). What such comparisons may do, and what they are meant to do, is to jolt us out of a particular misleading way of looking at the grammatical facts by concentrating our view upon a crucial contrast. This is intended to make it possible for us to take it in.34 But a glimpse of the landscape is not a representation of what is seen. It has been suggested that Wittgenstein’s remark that ‘It disperses the fog to study the phenomena of language in primitive kinds of application in which 34

‘Der Zweck des guten Ausdrucks und des guten Gleichnisses ist, dass es die augenblickliche Übersicht erlaubt’ (‘The purpose of a good expression or of a good simile is that it makes possible an instantaneous overview’) (MS 112 (Vol. VIII), 112v).

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one can command a clear view (übersehen kann) of the aim and functioning of words’ (PI §5; cf. BB 17) intimates that invented or simpliﬁed language-games are not merely fruitful objects of comparison, but also one form of a surveyable representation of some segment of our grammar.35 If that is what Wittgenstein meant, then it betokens a broadening of his conception of a surveyable representation since the idea originally occurred to him early in the 1930s. And if so, then it is surprising that he nowhere says this explicitly. Moreover, although the primitive language-games of §2 and §8 may indeed make it possible for us to obtain an overview (cf. MS 152, 91) of the aim and functioning of the words, and so disabuse us of the illusion that the essential function of words is to stand for things that are their meanings, it is not at all obvious that these simple language-games give us a surveyable representation of the grammar of the word ‘meaning’ or ‘the meaning of a word’ as these expressions are used in our language. They certainly do not ﬁt the original requirement of 36 TABULATING the grammatical use of words. Nor can it be argued that the description of a child’s use of such primitive forms of language when the child learns to talk gives us a surveyable representation of our use, even though it may well be highly illuminating to reﬂect on the primitive case. The description of the child’s primitive use of the ﬁrst ﬁve cardinals is not obviously a surveyable representation of the grammar of ‘cardinal number’, although, of course, it may illuminate some feature of it by way of contrast or similarity. Finally, the supposition that primitive language-games are surveyable representations of those fragments of grammar with which they are meant to be compared sits rather poorly with the geographical metaphors Wittgenstein commonly employs (see pp. 284f., 310n.) and with the accountancy metaphor of Z §273 (see below). For if what we are lacking is a map of the grammatical landscape that will enable us to ﬁnd our way around, then a map of a different, much simpler landscape will not answer that need, even though it may alert us to attend to the salient features of the landscape with which we are dealing. I suspect that the simple language-games introduced as objects of comparison are designed, as Wittgenstein himself said (see above), to clear the fog that envelops the landscape, and then, having an overview of the conceptual terrain, one may be able to give a perspicuous representation of the grammar of the problematic expression, geared to the solution or dissolution of the problems that beset one. Some further illumination comes from the few hints Wittgenstein gave. In a discussion of Hardy’s remarks on the inﬁnite, Wittgenstein wrote (in 1937) that the conception of the inﬁnite in the calculus of arithmetic is 35

I owe this suggestion to Dr Severin Schroeder. But one might claim that the grammatical propositions that the meaning of a word is (with appropriate qualiﬁcations) its use, that it is what is given by an explanation of meaning, that it is what is understood when the meaning of an expression is understood, and what is known when one knows how to use a word in accordance with its correct explanation do provide one with (at least the beginnings of ) a surveyable representation of the grammar of the phrase ‘the meaning of a word’.

36

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worth examining. The aim of such an investigation would be ‘a surveyable comparative representation of all the applications, illustrations, conceptions of the calculus.37 . . . The complete overview of everything that produces unclarity’ (MS 116 (Vol. XII), 55; cf. Z §273; quoted in full in Exg. §122, 2.1(iii)(i)). And he compared this to the way ‘a chartered accountant precisely investigates and clariﬁes the management of a business undertaking’ (ibid.). Here a surveyable representation appears to be an exhaustive, although also surveyable, description of everything that may be problematic about the grammar of an expression. It ‘lays out the grammar completely clearly’ (BT 417, see above p. 327). It is patently something far removed from a ‘redeeming word’ that illuminates, and from an invented language-game that functions as an object for comparison, or a helpful analogy that breaks the grip of a bad picture. It tabulates the rules for the use of words in a perspicuous manner that can readily be taken in. A chartered accountant does not provide a surveyable representation of the affairs of a business by a brief comparison with a different (more primitive) business down the road, even though such comparisons may be useful. Two earlier passages might seem to point in a different direction. (1) In the Diktat für Schlick (c.1931–3), Wittgenstein suggested that we can present in a simple way the grammatical relationship between the content and the intensity of belief if we replace the process of believing (sic) by the process of talking, and the intensity of belief by the strength and tone of voice. The ring of conviction offers us [the possibility of ] a simple, surveyable representation of the grammar of ‘conviction’ that is warranted for a large number of cases of use of the word. Replacing belief with its expression gives us at least a concise epitome of the grammar of ‘belief ’ (TS 302, 21). Wittgenstein goes on to clarify what he has in mind by means of an analogy. Imagine that chess were played only in chess notation on paper; then someone thinks of playing it with pieces on a board. Now one would be able to present the rules of chess in a much more readily surveyable manner than was possible before (see also MS 110 (Vol. VI), 130; PG 223). Puzzlement about the relationship between what one believes and the conviction with which one believes it is in effect puzzlement about the grammar of ‘conviction’ or ‘strength of belief ’. The grammar of ‘conviction’ is more readily illuminated by examining the relationship between saying what one believes and the manner in which one says it (the tone of voice) than by reﬂecting on ‘the process’ of believing (actually, there is no such thing) and its relationship to the intensity of the belief (which is not a sensation).38 But the chess analogy makes clear the inaccuracy of the remark in the Diktat. For it is obvious that substituting the expression of belief for the ‘process’ of believing no more gives one a surveyable representation of 37

Why ‘comparative’? Because to illuminate the grammar of the inﬁnite (e.g. of inﬁnite sets), we must compare it with the grammar of the ﬁnite (e.g. of ﬁnite sets), with which it is liable to be confused. 38 For Wittgenstein’s more considered (though still not ﬁnal) view, see BrB 144f.

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the grammar of conviction than replacing chess notation and paper by chess pieces and a chess-board gives one a surveyable representation of the rules of chess. Playing chess on a board with chess pieces is not a representation of the rules of chess, although it enables one to present them in a much more readily understandable manner than the previous way of presenting them by means of the syntactical rules of chess notation. What the substitution does, both in the case of the grammar of conviction and in the case of chess, is to make it possible to present the rules (in the former case, the grammar of ‘conviction’) so that they are easy to take in. (2) In an equally early (subsequently repudiated) passage in MS 145, 25f. (1933), Wittgenstein lists some tentative grammatical remarks about thinking (see Exg. §122, 2.1(iii(d))), for example, that thinking is operating with symbols, or operating with language, and that it is not essentially a mental process. Of these (grammatical) explanations he says that they are merely ‘clariﬁcations’ of the word; he then added, as an alternative wording, ‘surveyable representations’; ﬁnally, on the next line he wrote ‘representations’. This suggests that a well-chosen, illuminating grammatical proposition concerning a problematic term may be deemed a surveyable representation of its grammar. For some such grammatical propositions (rules) provide an epitome of the grammar of the expression — perhaps because they clarify (roughly) to what category the expression belongs (e.g. understanding is akin to an ability, and is not a state, process or activity (PI §§148–55)), or to what categories it does not belong (e.g. ‘to think’ is not an activity-verb (MS 124, 215)). MS 131, 68, observes that we commonly invoke a primitive picture to explain something conceptually puzzling. When we say, ‘Whoever says that, may mean the word thus or thus’, we think of meaning something as a mental activity that accompanies the saying and determines one or another relationship between the words uttered and reality. The explanation // Enlightenment // comes, Wittgenstein wrote, with a surveyable representation of something which is exceedingly difﬁcult to survey. Here, I conjecture, a surveyable representation of the grammar of ‘to mean something by something’ would be a judicious selection of grammatical propositions concerning meaning something by a word or sentence — a selection that can easily be taken in, and that will make it evident that the picture of an accompanying activity is misguided. So, for example, one might say that meaning someone by a name in an uttered sentence is not thinking of that person (for one cannot say, ‘While I said that I was meaning . . .’, but only ‘When I said that I meant . . .’), that meaning is not an act, activity or event (‘When I said that I meant . . .’ refers to the time of the act of saying, but not to a further act or activity performed at that time — otherwise it would make sense to ask how long it took, whether one had succeeded in meaning, and whether one found it easy or difﬁcult), and so forth (see Volume 4, ‘The mythology of meaning something’, sects 5–7). It appears evident that Wittgenstein was fairly relaxed about his (rare) use of the expression ‘a surveyable representation [of the grammar of a word]’. It

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evidently allows for a descriptive/grammatical interpretation — as a speciﬁcation, typically by means of grammatical propositions, of the salient rules (those necessary for the dispelling of speciﬁc conceptual difﬁculties) for the use of a given problematic expression in a manner that enables one to take them in, organized for the purpose of shedding light upon particular philosophical confusions. But perhaps it also allows for a comparative morphological interpretation and for a comparative language-game one. These alternatives should not be seen as exclusive. Taken as a ‘tabulating’ of salient grammatical propositions, the notion of a surveyable representation allows both a narrow and a broad interpretation. Narrowly understood, a surveyable representation of the grammar of an expression appears to be a grammatical proposition or a few grammatical propositions that shed enough light on the matter at hand to dispel illusion and to highlight the grammatical category or role of the expression in question. Broadly understood, a surveyable representation is a synopsis of the grammatical rules for the use of an expression (cf. MS 116 (Vol. XII), 55). Either way, the selection of the salient rules of grammar is guided by conceptual problems that arise in the domain in question. However, if the notion of a surveyable representation is taken broadly, then there is an obvious tension between the demands of comprehensiveness and the requirements of surveyability. This means that one must be judicious in one’s selection of grammatical propositions, choose those that are pertinent to philosophical problems that actually arise or are likely to arise, and avoid becoming bogged down in unsurveyable detail. That Wittgenstein saw a connection between his method and the morphological method that he associated with Goethe and Spengler is indisputable. It is also clear that he practices the technique of comparative grammatical morphology (in his sense) in the course of his philosophical investigations. What is not clear is whether such comparisons with associated concepts counts as part of a perspicuous representation or only as auxilary to such representations. Nothing of importance turns on this. Similarly, he does occasionally (but not often in the Investigations) construct simpliﬁed language-games as objects of comparison.39 He clearly thought that these facilitate the attainment of an overview of the grammar of problematic concepts. Are such language-games as (2) or (8) perspicuous representations of the grammar of the phrase ‘the meaning of a word’? This, I think, is doubtful. What is crucial is to see that the remark that the concept of a surveyable representation characterizes the way in which he looks at things in philosophy is intended to emphasize his employment of a very distinctive array of methods. These methods stand in stark contrast with the analytical methods advocated in the Tractatus, and with the methods of explanatory hypotheses 39

But often not so much to illuminate our existing grammar as to ﬁt some misconception of it, e.g. in the case of Augustine’s conception of language (PI §2) and in the case of Plato’s conception of simple elements (PI §48).

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employed in the sciences and mimicked in traditional metaphysics. What characterizes Wittgenstein’s new philosophy is clariﬁcation of conceptual problems by descriptions of grammar and by comparative grammatical morphology. And one feature of its practice is the judicious introduction of simple or simpliﬁed language-games that illuminate our conceptual structures. It might be objected that construing surveyable representations as tabulating the grammar of expressions in a surveyable manner in order to dissolve philosophical problems has the absurd consequence that something Wittgenstein declares to be the hallmark of the form in which he presents his philosophical investigations is in effect barely ever practised. This is clearly wrong on one interpretation. Specifying the grammar of problematic expressions, I have suggested, can be taken narrowly or broadly. If construed narrowly, it is easy to ﬁnd numerous examples of his perspicuously presenting the grammar of expressions. He tells us that colour samples should be counted as among the instruments of language (PI §16). He reminds us that naming is preparatory to the use of a word (PI §26), but not itself a move in the language-game (PI §49). He points out that a sample is a paradigm, something with which comparison is made, that it is not described by an ostensive deﬁnition (PI §50), hence that it is not a point at which language is ‘connected to reality’, but belongs to the means of representation; that understanding is not a mental state but is akin to an ability (PI §150 and p. 59/50n.); that to mean something is not the same as to think of it (PI §187); and so on. If we take the notion broadly, as Wittgenstein’s geographical metaphors invite us to do (see above, pp. 310n., and ‘Philosophy’, pp. 284f.), it is true that he rarely practices what he preaches.40 The exception to the rule is his plan for the treatment of psychological concepts (Z §§472ff.). Of this readily surveyable morphological investigation he wrote: ‘It can answer a series of different philosophical problems. It is a method of getting clear about various conceptual difﬁculties’ (MS 134, 156). And so indeed it is. But, illuminating though this sketch is, he never actually executed the plan. And there are no further examples of such systematic tabulations of grammatical propositions. Can this oddity be explained? He said of himself in his lectures, ‘In order to be a good guide, one should show people the main streets ﬁrst. But I am an extremely bad guide, and am apt to be led astray by little places of interest, and to dash down side streets before I have shown you the main streets’ (LFM 44). So, in his investigations into the will and voluntary action (PI §§611–28) his primary concern is with disentangling the muddle that besets us when we think that willing must be either something we do or something that happens to us. In his investigations into intentions he is primarily concerned with what one remembers when 40

But perhaps this is no odder than the fact that in the Tractatus, the standard-bearer of the method of analysis, there are (with the exception of the account of tautologies of logic) no actual analyses of any propositions whatsoever.

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one remembers that one was going to do something (PI §§629–60). In these and other cases, his compressed discussions have an unprecedented depth and manifold ramiﬁcations, which will be examined in the course of this Commentary. But they do not give one, or promise to give one, perspicuous representations (in the broad sense) of the grammar of the expressions under consideration. He was too concerned with dashing down the side-streets — especially if they were streets in which he had got lost when he was writing the Tractatus. On the other hand, scattered throughout his voluminous notes we often ﬁnd numerous grammatical observations that can be used by the judicious cartographer who has the inclination to master the geography of concepts (MS 137, 63a) and to draw such maps as will enable others to ﬁnd their way around the seas of language and to avoid becoming stranded on the reefs of grammar.

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

XVI Truth and the general propositional form 1. The demands of the picture theory In 1915 Wittgenstein wrote, ‘My whole task consists in explaining the nature of the proposition, i.e. in giving the nature of all facts, whose picture the proposition is. In giving the nature of all being’ (NB 39). This is an extraordinary remark. The objective — to give the nature of all being — is as sublime a goal as any metaphysician can conceive (cf. PI §§89f.). The idea that this can be achieved by an investigation of the nature of the proposition, i.e. the sentence in its projective relationship to the world, marks the ﬁrst steps of the linguistic turn in twentieth-century philosophy. It is noteworthy that an alternative title that Wittgenstein considered for Logisch-philosophische Abhandlung was Der Satz (The Proposition). Clarifying Wittgenstein’s reasons for this bold step will also make clear his early account of the proposition, and the manner in which the concept of a proposition was held to be determined by common properties. His conception of the proposition was crystallized into the claim that the general form of the proposition is ‘Es verhält sich so und so’ (‘This is how things stand’, or ‘Thus-and-so is how things are’). This formula or schema needs to be clariﬁed in order to understand his later criticisms of the essentialist idea that informs it. This in turn is a prerequisite for understanding his later conception of the relationship between the proposition, on the one hand, and truth and falsehood, on the other. The central themes of the Tractatus were the metalogical conditions of the possibility of representation and the nature of logic and logical necessity. The elucidation of the former was to be the means to illuminate the latter. The distinction between what can be said and what can be shown but cannot be said, on which Wittgenstein was ﬁnally to put so much emphasis (CL 68; and letter to von Ficker, September or October 1919), emerged from consideration of these two main themes of the book. Reﬂections upon the general conditions of symbolic representation were the form in which fundamental problems about the intentionality of thought and language were articulated. The manner in which Wittgenstein presented these was by way of two related puzzles: ﬁrst, how can it be that a false proposition (a sentence with a sense) has a sense (is meaningful), and secondly, how one can believe what is not the case? (It was only after his return to philosophy in 1929 that he presented

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the problems of intentionality by means of the question of how an expectation can anticipate its fulﬁlment.) Puzzlement over how a proposition (a linguistic item) can be false yet have a meaning arises from the natural (but confused) thought that a proposition is false (and its negation true) when no fact corresponds to it. But if no fact corresponds to it, how can it be meaningful? After all, it represents a fact; and if there is no fact for it to represent, then it represents nothing; and if it represents nothing, then it is meaningless. (This, from the perspective of later philosophers who have the beneﬁt of standing on the shoulders of those who fought their way free of this confusion, appears crude, as Wittgenstein himself noted (AWL 108).) Puzzlement over how one can believe what is not the case arises, however, in a more subtle way. If I believe that p, and my belief is true, then what I believe is indeed the case. For what I believe is not something distinct from what is the case — such as a Fregean thought or a proposition, which stands in some obscure relation to what is actually the case. My belief does not fall short of what is the case. However, if I believe that p, and my belief is false, then what I believe is not the case – it does not obtain at all. But that, as Socrates pointed out to Theaetetus, surely does not imply that I believe nothing. What I believe when I believe truly that p and what I believe when I believe falsely that p is exactly the same. But how can that be? How can what I believe be both what is the case if it is true that p, and distinct from what is the case if it is false that p, and yet be the same in both instances? The problem was intended to crystallize the very general question of the essential relation that must obtain between thought and reality, and between language and reality, which makes it possible for propositions to do the extraordinary thing they do: namely, to depict reality truly or falsely (cf. PI §93).1 The picture theory of representation was Wittgenstein’s solution to the question. A proposition is essentially a logical picture of a state of affairs — it depicts a state of affairs, which may or may not obtain. The logically simplest kind of proposition, which has no logical complexity but is, rather, an immediate combination of names, is an elementary proposition. An elementary proposition, Wittgenstein thought, is logically independent of every other such proposition. It can be true or false as the case may be, and everything else remain the same. The obtaining of a state of affairs is a positive fact. The non-obtaining of a state of affairs is a negative fact. A proposition is true if things are as it depicts them as being. So the proposition that p is true if the state of affairs it depicts obtains (TLP 4.062), i.e. if it is a fact that p. It is false if the state of affairs that it depicts does not obtain, i.e. if it is a fact that not-p. 1

As so often in philosophy, the mistake takes place before the beginning — in the presuppositions of the questions. It was only after 1929 that it dawned on Wittgenstein that this seemingly deep question is misconceived. For, in the intended sense, there is no such essential, metalogical relation between language (or thought) and reality.

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The constituents of an elementary proposition are simple names. The simple names are correlated with simple objects as their meanings. Simple objects are the indestructible substance of the world. They have internal and external properties. Their external properties are their contingent concatenations with other objects to constitute a fact. Their internal properties are their combinatorial possibilities, which constitute their ontological category. The combinatorial possibilities of the simple names in accordance with logical syntax reﬂect the metaphysical combinatorial possibilities of the objects that are their meanings. A possible combination of names constitutes a sentence with a sense — a logical picture of a possible state of affairs. There are perfectly general constraints on the possibility of representation (Wittgenstein was later to refer to these ideas as a ‘metaphysics of symbolism’). Only simple names can represent simple objects, only relations can represent relations (in ‘aRb’ it is not ‘R’ that represents the relation in which a and b stand to each other, but rather it is ‘R’’s standing thus between ‘a’ and ‘b’ (in this form of representation)). And only facts can represent facts. For the propositional sign itself is a fact. The sense of a sentence is its agreement and disagreement with the possibilities of the obtaining and non-obtaining of states of affairs (TLP 4.2). For an elementary sentence ‘p’ agrees with the obtaining of the state of affairs that p and disagrees with its non-obtaining, both of these being possible. The object of one’s belief that p is the possible state of affairs that p. What one thinks, when one thinks truly that p, and what one thinks when one thinks falsely that p is exactly the same possibility, which, in the one case, obtains (is actualized, realized, i.e. is a fact), and in the other does not. That there is such a possibility is guaranteed by the meanings of the simple names that are constituents of the proposition. For the simple names cannot fail to refer, since their meanings are part of the sempiternal substance of the world. Moreover, since what corresponds to a simple name (or concept-word) is exactly one determinate thing — a simple object (which may be a property or relation too), each elementary proposition depicts an absolutely speciﬁc state of affairs. The conception was subtle and reﬁned — a form of modal realism; i.e. it was committed to the thought that logico-metaphysical possibilities are independent of language and determine the range of all possible worlds. It apparently resolved the deep problems over which, in the young Wittgenstein’s view, the philosophies of Frege and Russell had come to grief. But its commitments, logical, ontological and metaphysical, were extensive and anything but trivial. They all seemed to ﬂow from the presuppositions of logic: namely, that names have meanings and that propositions have sense (TLP 6.124). But these presuppositions are not innocuous. They seemed to make unavoidable a very particular conception of the meaning of a name and an equally speciﬁc (and idiosyncratic) conception of sense. The conception of meaning was Augustinian, taking the meaning of a name to be the object in the world which the name represents. The structure of a sentence determines a sense — roughly speaking, the possibility depicted — and there can be no such thing as an

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indeterminate sense. For there are no indeterminate states of affairs. So what a proposition depicts it must depict clearly — a thought that meshed perfectly with the demands of logic. For determinacy of sense seemed to be a prerequisite for logic. Unless sense is determinate, it seemed, the laws of logic would not apply to propositions. But the laws of logic are not laws for some as yet uninvented or ideal language. Nor are they laws for thoughts that are independent of language. Logic is the transcendental condition of representation, and hence too of language and thought. This in turn seemed to make unavoidable a particular conception of analysis. Analysis, it seemed, must terminate in elementary propositions the constituents of which are simple names, whose meanings are indestructible simple objects. This ensured determinacy of sense, and excluded the possibility of reference-failure. Frege had thought the truths of logic to be universal generalizations. They were the content-indifferent laws of thoughts (i.e. propositions, Platonistically conceived) — hence valid for all thoughts. Russell likewise held that the laws of logic were generalizations, but he thought that they were descriptions of the most general facts in the universe — so logic was the most general investigation of reality. Wittgenstein held both to be wrong. The mark of a proposition of logic is not generality at all (TLP 6.1231); it is necessity. Logical truths are propositions that could not be false. So, ‘Either it is raining or it is not raining’, contra Frege and Russell, is a logical truth. Against the background of the picture theory of representation, he gave an account of the nature of logical propositions not as generalizations but as tautologies. Every elementary proposition is bipolar; i.e. it is capable of being true and also capable of being false. Since ‘It is false that p’ is equivalent to ‘not-p’, every elementary proposition can be negated, and its negation is a proposition with a sense. Any members of a set of elementary propositions can be successively asserted. So both negation and conjunction are given together with the mere idea of an elementary proposition as such. But if negation and conjunction are given, then so too are all the other logical operations: namely, disjunction and conditionality (and, Wittgenstein supposed, also quantiﬁcation). So all forms of truth-functional combination are reducible to the operation of joint-negation on any given set of elementary propositions. Successive applications of the operation of joint-negation will generate all possible truthfunctional combinations of the given set of elementary propositions. If there are n elementary propositions, they will allow 2n truth-functional combinations. For any set of elementary propositions there are two limiting cases: tautologies, which are true for every possible assignment of truth-values to the constituent propositions, and contradictions, which are false for every possible assignment. So the truths of logic are unconditionally true, i.e. necessarily true. They say nothing at all about the world, precisely because they are true no matter what truth-values their constituents have, i.e. no matter how things are in the world — so they delimit the world in no way. Since they say nothing at all, they can be described as senseless (they have, as it were, zero sense). So,

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pace Frege and Russell, there can be no science of logic, consisting of the propositions of logic with a subject matter of their own, and the establishment of which is a cognitive achievement. With this elaborate metaphysical picture before us, it should no longer be surprising that Wittgenstein thought that the investigation of the logic of the proposition should be an investigation of the essence of description, and that this in turn should be tantamount to an investigation of the essence of the world. It should also be evident that this remarkable metaphysical structure was wholly dependent upon the thought that all propositions share common properties in virtue of which they can do what they do: namely, depict — truly or falsely — how things stand. These common properties determined ‘the general propositional form’ (TLP 4.5). This, he thought, could be given by a description of the propositions of any sign-language whatsoever in such a way that every possible sense can be expressed by a symbol satisfying the description, and every symbol satisfying the description can express a sense, provided that the meanings of the names are suitably chosen. It is clear that only what is essential to the most general form of a proposition may be included in its description — for otherwise it would not be the most general form. The existence of a general propositional form is proved by the fact that there cannot be a proposition whose form could not have been foreseen (i.e. constructed). The general form of a proposition is: This is how things stand.

The argument of the third paragraph is that it is unintelligible that we should come across a form of words which we could recognize as expressing a sense, but of which we could also say that it could not be foreseen that such an expression constitutes a proposition, i.e. that it is not implicit in the rules of logical syntax that this is a proposition. Otherwise, in order to recognize this new proposition as having a logical form of a proposition, hence as expressing a sense, one would presumably have to have some unique experience, a ‘logical experience’, in virtue of which one recognized that this unforeseeable expression is a proposition. But that is absurd. Further elaboration is given to the conception of the general propositional form by the explicit speciﬁcation of the thesis of extensionality: ‘All propositions are results of truth-operations on elementary propositions’ (TLP 5.3). So Wittgenstein subsequently (TLP 6) equates the general propositional form ¯ )], on the assumption that with the general form of a truth-function [ p¯, ¯ξ, N(ξ an elementary proposition can, formally speaking, be represented as a truth¯ )] says is that all propositions function of itself (TLP 5). For what [ p¯, ¯ξ, N(ξ can be generated from elementary propositions by successive applications of the N-operator (of joint-negation). The general propositional form — ‘This is how things stand’ — seems at ﬁrst sight empty and trivial. But in the context of the picture theory and the metaphysics of atomism, it is anything but that. Indeed, it is the precipitate of

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the picture theory of representation. So what are the common properties alleged to be shared by all propositions with a sense? We may list them as follows: 1 2

3

4

5

6 7 8

Every proposition is a picture of a possible state of affairs Every proposition is complex — a structure of simple names concatenated in accordance with logical syntax. (This feature is captured by the formulation ‘das und das — so und so — ist’ (‘Such-and-such is thus-and-so’) in §95.) Every proposition with a sense (but not tautologies and contradictions, which lack sense) is bipolar, i.e. capable of being true and capable of being false. This reﬂects the essence of states of affairs: namely, that they may obtain or fail to obtain. The sense of a proposition is its agreement with the state of affairs the obtaining of which makes it true (and the non-obtaining of which makes it false) and its disagreement with the state of affairs the obtaining of which makes it false (and the non-obtaining of which makes it true). Every proposition is a fact, since it is the fact that the names are concatenated in the structure in which they are that says that things (the meanings of the names) are thus concatenated in reality. A proposition is true if and only if things are as it depicts them as being. Elementary propositions are logically independent. Every proposition is a truth-function of elementary propositions.

In addition to these theses are various claims concerning what is shown by a proposition, but cannot be said. These need not concern us here.

2. ‘That’s the way the cookie crumbles’ The criticisms in the brief discussion of the general propositional form in the Investigations can be separated under three headings. First, Wittgenstein examines what kind of error was involved in dubbing ‘Es verhält sich so und so’ the general form of a proposition. This expression is a decent German sentence, and we should look to its normal use — for that is where he took it from. He had in effect sublimated it. So, we must ‘bring words back from their metaphysical to their ordinary use’ (PI §116). Second, he argues that, contrary to his early preconceptions, there is no such thing as ‘the general propositional form’. Our concept of a proposition is not an ineffable, super-categorial one. Like the other concepts that he had treated in the Tractatus as metalogical, it has a perfectly decent use. But it is not deﬁned by characteristic marks. Nor is ‘proposition’ the name of something simple and unanalysable that is explained by a paradigm (as are colour-words). There are no common properties in virtue of which we denominate something ‘a proposition’. Rather, the concept of a proposition is a family-resemblance concept.

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Third, arguing that all that was really captured by his early formulation of the essence of the proposition was that a proposition is whatever is true or false, he examines the relationship between ‘proposition’ and ‘true’ and ‘false’ in order to establish that the concepts of truth and falsehood are not criteria for something’s being a proposition (cf. AWL 140). So, granting that a proposition is whatever is true or false does not show that the concept of a proposition is not a family-resemblance one. Other criticisms — e.g. of the thesis of extensionality, of the picture theory of representation, of the independence postulate, of the ontology of simple objects, of states of affairs and facts — are either to be found elsewhere in the book, or in other writings. Wittgenstein came to think that the idea of the general propositional form was a typical philosophical illusion (cf. Exg. §104). It was rooted in preconceptions concerning what names and propositions must be like. He had thought that names must really be simple. The real name must have no sense or connotation, but only a meaning, and its meaning is the entity it stands for. So the general form of a name seemed to be represented by the demonstrative ‘this’, which has no connotation, and which is used to make a connection between language and reality (cf. NB 61). A similar preconception was associated with the general concept of the proposition. Every proposition must be a (logical) picture; otherwise it would not be capable of doing what all propositions do: namely, representing — representing both how things are and how things are not (see Exg. §93). So, the young Wittgenstein had drifted unselfconsciously into the force-ﬁeld of the Augustinian conception of language: the essence of names is to have a meaning; the meaning is correlated with the word, it is the object for which the word stands (PI §1 and Exg.); and the essence of sentences is to describe (see ‘The Augustinian conception of language’, sect. 2e). This was not a discovery but a requirement. And anything that failed to satisfy it had to be reducible to something that does satisfy it, or to be excluded from the category of genuine propositions. So propositions of arithmetic and geometry had to be pseudo-propositions (TLP 6.2). What Wittgenstein was later to call ‘grammatical propositions’, such as ‘1 is a number’ or ‘red is a colour’, had to be ill-formed, and were held to be futile attempts to say something that can only be shown. Propositions of ethics and aesthetics were held to be nonsensical attempts to say what cannot be said. All this he was later to castigate as ‘dogmatism’. There is a perfectly decent analogy between certain kinds of proposition (understood, following Wittgenstein, as a sentence with a sense) and pictures. Just as one may say of a painting that it represents Napoleon’s crowning of Josephine, so too one may say of the proposition ‘The bottle is to the left of the glass’ that it represents a certain conﬁguration of a particular bottle and glass on a table. Here the expression ‘the bottle’ stands for this + bottle, the expression ‘the glass’ stands for this + glass, and that the expression ‘is to the left of ’, ﬂanked as it is by the other two expressions, represents the relation

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in which the bottle stands to the glass (namely, being to the left of it). Just as the history painting depicts an event, so too the proposition is a logical depiction of a state of affairs. But this is just an analogy. And, like all analogies, it goes only so far. Any painting corresponds not to one proposition but to indeﬁnitely many (what David’s painting of the Napoleonic coronation depicts would take pages to describe, and the description could be extended indeﬁnitely). Even the simplest of Morandi’s paintings depicting a bottle and a glass on a table corresponds to an indeﬁnite multiplicity of propositions. Furthermore, there is no analogue, in the case of a painting, of the expression ‘is to the left of ’. For the painted bottle’s standing to the left of the painted glass is not a symbol that signiﬁes the relation of being to the left of.2 Furthermore, while there is an analogy in the case of certain kinds of proposition, it does not hold for others. It is quite wrong to suppose that the function of every proposition, even within the class of bipolar propositions that Wittgenstein considers, is to describe a state of affairs consisting of a concatenation of objects (no matter how generously we take the term ‘object’). As Wittgenstein remarked, does ‘It is raining’ say that things are concatenated thus-and-so (Z §448)? Does it have the property of raining? Is ‘It is raining’ a logical product, and so analysable into a set of elementary propositions (VoW 245)? Does ‘I’ll go’ describe a concatenation of objects? Am I one of them? Is going another? ‘Es verhält sich so und so’ is supposed to be the general form of the proposition. It intimates that propositions are essentially complex (as is evident in the German of PI §95). Philosophical logicians working in the Aristotelian tradition argued that propositions are composed of subject and predicate. For the role of the proposition is to afﬁrm (or deny) the conjoining of distinct ideas. The Fregean tradition, in which the young Wittgenstein worked, repudiated the subject/predicate form of Aristotelian logic, but likewise insisted on the essential complexity, and hence compositionality, of the proposition. Every sentence that expresses a thought (proposition), Frege held, decomposes into the name of a function and the name of an argument, which argument the function maps on to a truth-value. Russell and the young Wittgenstein agreed that the sentence essentially decomposes into function-name and argument-name, but held that the value of the propositional function is the proposition itself, not a truth-value. But, as Wittgenstein came to realize, it is mistaken to suppose that the proposition is essentially complex. Can a gesture not express a proposition (e.g. Sraffa’s Neapolitan gesture of contempt, or the shrugging of

2

Wittgenstein was also wrong to suppose that the linguistic expression ‘is to the left of ’ being ﬂanked by the ordered pair of names ‘the bottle’ and ‘the glass’ stands for or is the name of the relation of being to the left of. If anything is such a name, it is the expression ‘the relation of being to the left of’. There are further disanalogies too, since, in one sense, the ﬁgure in the painting does not represent or stand for Napoleon, but is Napoleon — but these complications concerning the forms of description of pictorial representation need not concern us now.

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one’s shoulders)? Is it only a proposition when translated into word-language? One-word sentences, of course, are not ‘complex’. They can be said to be elliptical — relative to other sentences in our language by which they might be paraphrased (PI §§19f.). But we can readily imagine a primitive language in which there are various one-word sentences, without there being any possibility of paraphrase in that language. So it is not of the essence of the proposition to be complex. Rather, complexity is a characteristic feature of very many types of proposition that belong to the family of propositions — it is, one might say, a salient ‘centre of variation’. Moreover, complexity is an essential feature of certain forms of presentation of propositions for certain purposes: e.g. the forms of syllogistic and of the function-theoretic predicate calculus that we adopt for logical purposes of perspicuously displaying arguments. Comparability with reality for truth or falsehood had appeared to be a common feature of all propositions with a sense. For the sense of a proposition was construed as its agreement and disagreement with the obtaining and non-obtaining of states of affairs. With regard to any proposition with a sense, one cannot tell, merely by looking at it, whether it agrees with reality or not. One must compare it with reality, i.e. verify it, to ﬁnd out whether it is true or false. But this too distorts the phenomena. While it is obscure what Wittgenstein thought of the analysis of ﬁrst-person experiential propositions when he wrote the Tractatus, it is striking that in his brief phenomenological phase in 1929/30, he held that ﬁrst-person psychological propositions are the ‘genuine’ propositions that get compared with reality and are thereby conclusively veriﬁed or falsiﬁed, whereas other empirical propositions, about objects around us or about other people, are ‘hypotheses’ that can never be conclusively veriﬁed or falsiﬁed. This conception rapidly crumbled — indeed, was turned on its head. For ‘I have toothache’, ‘I want a drink’ or ‘It looks to me just as if things are thus-and-so’ are paradigms of propositions that do not get compared with reality for veriﬁcation or falsiﬁcation. Here, truthfulness guarantees truth (cf. PI p. 222/189).3 Bipolarity is indeed an important feature of many kinds of proposition. It is not a feature of propositions of mathematics and logic or of grammatical propositions. Nor is it a feature of propositions concerning absolute value. But, contrary to the Tractatus, that is no reason for dogmatically insisting that they are not genuine propositions. So, conﬁdence in the idea that the concept of a proposition is characterized by a set of common properties waned. With it came doubts about the role in which the sentence allegedly expressing the general propositional form was cast. ‘Es verhält sich so und so’ is itself a German proposition, just as ‘This is how things stand’ is an English one. They have a determinate use and are not, as 3

Of course, the corresponding third-person propositions, e.g. ‘He has toothache’, do get compared with reality for veriﬁcation, and a person’s utterance ‘I have toothache’ is a criterion in the circumstances for the truth of the proposition that he has toothache.

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it were, on the Index — representing strictly ineffable forms. But they are not ‘compared with reality’ for agreement and disagreement. On the contrary, they are used to refer anaphorically to something already said or to refer to something about to be said, and it is what can be compared with reality for agreement or disagreement. We may say, ‘He explained his position to me, said that this was how things were, and that therefore he needed an advance’ (PI §134). But ‘this is how things are’ has this role only because it has the structure of an English sentence. It functions as a propositional schema. We would not use the letter ‘p’ (as in the notation of formal logic) for such purposes, but we can readily imagine such a convention. It would permit us to say, ‘He explained his ﬁnancial situation, said that p, and that therefore he needed an advance.’ But that would not tempt us to think that the letter ‘p’ expresses the general propositional form. Equally, one can imagine a sentence with sense functioning, in the appropriate context, as a propositional schema for the same purpose. So we might use ‘The sky is blue’ thus (MS 142, §117). Indeed, this is how the sentence ‘That’s the way the cookie crumbles’ is used in American slang (albeit with a tinge of resignation). For Americans can indeed report: ‘He explained his position to me, said that that’s the way the cookie crumbles, and that therefore he needed an advance.’ But would anyone claim that ‘That’s the way the cookie crumbles’ expresses the general propositional form?

3. ‘. . . do we have a single concept of proposition?’ (PG 112) In Investigations §134, Wittgenstein observes that the propositional schema ‘This is how things are’ was chosen to fulﬁl the role of the expression of the general propositional form because it is itself an English sentence. It is used as a propositional schema for purposes of anaphoric or cataphoric reference to something said. It has that role because it has the structure of an English sentence. But one could, in principle, choose the propositional variable ‘p’ to fulﬁl that role. But it would not sound right to say that ‘p’ is the expression of the general form of the proposition. So, Wittgenstein concludes ironically, one feature of our concept of a proposition is sounding like a proposition. To be sure, propositions (sentences with a sense) have a characteristic propositional jingle (Satzklang). But this is neither necessary nor sufﬁcient for being a proposition. It is not necessary, since we can readily conceive of a language which differed from English only in inverting the word-order (AWL 100). This would lack the characteristic jingle, but, since it would possess the identical logical multiplicity of English, its sentences could express propositions nevertheless. If we were to learn it, its sentences might assume a characteristic intonation. But they might not; and even if they did, it would not be as a consequence of this that we attribute propositional status to such strings of symbols. The propositional jingle is not sufﬁcient for being a proposition either.

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Many sentences, especially in philosophy, have the right jingle, but do not express propositions. Very often they are latent nonsense, which it is the task of philosophy to render patent. So, do we have any general concept of a proposition? Wittgenstein’s answer is negative (PG 112; BT 61). The concept of a ‘proposition’ lacks the formal unity ascribed to it in the Tractatus. It is a family of structures related to one another in complex ways (PI §108). This is evident from the fact that we explain the concept ‘proposition’ by means of examples (PG 112). For this reason we might say that ‘proposition’, like ‘number’, is not sharply deﬁned. We could give it sharp boundaries if we wished. But we do not do so, for we have no need to (PG 117). Lack of sharp boundaries does not infect the centre with uncertainty. If the boundaries of the concept of a proposition are indeterminate, how do we determine, of a new kind of proposition, that it is a proposition (PG 113)? Only by analogy — and nothing forces our hand. Singular observationstatements, psychological statements, ﬁrst-person psychological attributions, mathematical equations, statements of applied mathematics, statements of laws of physics, tautologies, contradictions, propositions of ethics, these and numerous other categories are related by a web of similarities and analogies which could not be constructed or predicted in advance (PG 117). Indeed, when Wittgenstein’s strictures fall upon some category or other, e.g. the result of preﬁxing ‘I know’ to an avowal, what he is doing is simply stressing disanalogies commonly unnoticed by philosophers who want to draw special philosophical conclusions from such apparent propositions. The disanalogies provide a ground for challenging those conclusions. So ‘I know’ can function as an epistemic, proposition-forming operator on propositions only where ‘I don’t know whether’ can too. For it adds something to what is conveyed by the proposition it operates on: namely, it excludes ignorance. But if there is no such thing as ignorance in certain cases (e.g. ‘I have a pain’), then there is nothing to exclude — no epistemic work for the operator ‘I know’ to do.4 So the result of preﬁxing it is either nonsense or mere emphasis (PI §246). ‘Proposition’, like ‘number’, is not deﬁned once and for all by drawing sharp boundaries. Nor does our explanation of the meaning of ‘proposition’ have to distinguish propositions from everything else, including cabbages and kings. A deﬁnition of ‘number’ which does not rule out Julius Caesar from being a number is not, pace Frege, therefore defective. We could not confuse Julius Caesar with a number, or a cabbage with a proposition, for nothing would count as having confused the one with the other. So we do not need a deﬁnition to 4

This does not mean that there is, in certain cases and circumstances, no non-epistemic work for ‘I know’ and ‘I don’t know’ to do. ‘I don’t know what I want’ is normally used to signify indecision, not ignorance. There should be nothing surprising about epistemic terms having nonepistemic uses. ‘While he was talking I forgot my pain (or my troubles) completely’ does not indicate a lapse of memory, but a distraction of attention.

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stop us from doing something that cannot be done anyway. We do need, occasionally, to distinguish one type of proposition from another and to explain why we distinguish them. This we can generally do. For example, we may distinguish tautologies from non-tautologous propositions. Sometimes, especially in philosophy, we need to distinguish a proposition from something that looks or sounds like one, but isn’t. This too can be done, by showing that it lacks sense. This typically requires a careful examination of analogies and disanalogies of precisely the kind Wittgenstein engages in so frequently.

4. ‘. . . the use of the words “true” and “false” . . . belongs to our concept “proposition” but does not ﬁt it . . .’ (PI §136) One obvious objection to the contention that proposition is a family-resemblance concept is examined by Wittgenstein. For surely, it is a common property of anything we call ‘a proposition’ that it has one or the other of the two truthvalues. So why cannot the concept of a proposition be sharply circumscribed in terms of the property of bearing truth-values? Wittgenstein links this issue with the conception of the general propositional form. The Tractatus conception of the general propositional form was just a confused way of saying that a proposition is whatever is true or false. For instead of saying ‘Such-and-such is the case’ gives the general propositional form, he could have cited the sentence ‘Such-and-such is true’, for the latter fulﬁls much the same function as the former (PI §136). We use ‘It is true that p’ or ‘Such-and-such is true’ to refer to something that has been said or is envisaged as being said, and to afﬁrm it — and what we thus refer to is precisely the proposition that was expressed or is envisaged as being expressed. So now it appears that we can deﬁne a proposition: as whatever can be true or false. In response, Wittgenstein asserts that ‘p’ is true = p ‘p’ is false = not-p

On this he makes no comment. It is, one must admit, badly phrased. In the ﬁrst place, ‘ “p” is true’ (e.g. ‘ “Rome is in Italy” is true’) is not a well-formed English sentence, since the truth-predicate demands a nominal as subject (and it is not sentences that are true or false, but what is said by their use). This is readily rectiﬁed by replacing the above disquotational formulae by the following denominalization formulae: ‘It is true that p = p’ or ‘That p is true = p’

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‘It is false that p = not-p’ or ‘That p is false = not-p’.5

Furthermore, the use of ‘=’ must be taken to signify deﬁnitional equivalence. In the Investigations, Wittgenstein neither explicitly endorses nor explicitly denies the view that the truth-operator (or truth-predicate attached to a sentence appropriately nominalized for it) is redundant. But his endorsement of the disquotational or denominalization formulae gives support to the interpretation that he thought that by asserting that it is true that p one is saying no more than one is saying by asserting that p — and that, under one interpretation of the so-called Redundancy Thesis, is to embrace the Redundancy Thesis that the two sentences express the very same proposition. This interpretation is further supported by the explicit claim in The Principles of Linguistic Philosophy that ‘It is true that p’ says no more than the plain ‘p’ (PLP 30f.; cf. MS 154, 31r).6 In his lectures in 1939, Wittgenstein explicitly remarked: ‘To say proposition p is true [sic] is just the same as to say p’ (LFM 68; cf. 188). On the other hand, it is clear from the Principles that Wittgenstein (assuming that Waismann is reporting him) had noted that ‘p’ and ‘It is true that p’ are not used in the same circumstances. We use ‘It is true that p’, Waismann wrote, only when, for example, we want to reject a doubt on the matter, or when summing up the conclusion of an argument.7 This suggests that Wittgenstein, under a different but perfectly reasonable interpretation of ‘redundancy’ that pertains to circumstances of appropriate utterance, did not accept that the truthoperator is redundant. Certainly, Wittgenstein’s dictation to Waismann (VoW 493, discussed below) suggests that he thought that the story considerably longer and more subtle than the brief Redundancy Thesis would have us believe. What is clear is that the point of the remark in §136 is to emphasize that the concept of a proposition is not characterized, or not informatively characterized, by the common property of being either true or false. To say that a proposition is whatever can be true or false, Wittgenstein claims, amounts 5

In the Grammar Wittgenstein did note the following: ‘It can also be put thus: The proposition “ ‘p’ is true” can only be understood if one understands the grammar of the sign “p” as a propositional sign; not if “p” is simply the name of the shape of a particular ink mark. In the end one can say that the quotation marks in the sentence “ ‘p’ is true” are simply superﬂuous’ (PG 124). But this too is not quite right yet, since ‘Rome is in Italy is true’ is not a well-formed English sentence either. Both the truth-predicate and the truth-operator need the nominal clause ‘that p’. Nevertheless, the remark intimates that Wittgenstein veered away from the disquotational view that his formula suggests and towards the acceptable denominalization formula. This is supported by an observation in MS 116 (Vol. XII), 110, in which he seems to be challenging the disquotational account: ‘The proposition (Satz) “It is raining” surely states something about the weather but nothing about the words I utter. But then how can “It is raining” say the same as: “The proposition (Satz) ‘It is raining’ is true”, since it does state something about the words?’ 6 ‘Saying more’ is explained thus (PLP 30f.): the proposition ‘p’ says more than the proposition ‘q’ if ‘~ p . q’ is meaningful (possible) but ‘p . ~ q’ is inconceivable (contradictory). 7 The list of warranting circumstances could be lengthened, e.g. to conﬁrm something already stated by another; to concede that p, preparatory to advancing an objection of some kind; to anticipate what someone may assert, in order to put it aside; and so on.

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to no more than saying that we call something a proposition when, in our language, we apply the calculus of truth-functions to it. (He disregards the deviations of the rules for the connectives in the calculus from the rules for ‘not’, ‘and’, ‘or’, ‘if . . . , then . . .’ in natural language. But perhaps that does not matter, since what he has in mind is primarily that we call something a proposition when it is the kind of expression that can be operated on by these operators and by the truth-operator.) In the Grammar he observed that the expression ‘how things stand’ (‘Es verhält sich . . .’) in the schema he had chosen to express the general propositional form was really no more than a handle for truth-functions. So it merely indicates which part of speech comes into play: namely, a declarative sentence (PG 124). Conceding that we can formally deﬁne a proposition as whatever can be true or false does not imply that being true and being false are criteria by reference to which we can determine whether or not something is a proposition, as being married and being a man can be used to determine whether or not someone is a bachelor. One cannot put words together and then add ‘is true’ as an experiment, so that if the result makes sense, then the combination of words expresses a proposition (PG 124). For being true or false are not properties of propositions as being red or green are properties of fruits (AWL 140).8 That propositions can be true or false is not a discovery like ‘iron can rust’. It is a rule for the use of the word ‘proposition’ (indeed, one could say that this rule is given by the rule ‘p v ~ p = Taut’). So all it amounts to is that what we call ‘a proposition’ is also what can be said to be either true or false (ibid.). Wittgenstein spells out an analogy (PI §136): it is as if we were to say, ‘The king in chess is the piece one can check’. But in so far as this looks as if it speciﬁes a means of identifying the chess king, it is misleading. For it just means that in chess we check only the king. It gives a rule of the game, not a means for identifying the king. Similarly, we may grant (at any rate for present purposes) that everything we call a proposition is either true or false, as indeed we may grant that any activity (such as cricket, bridge or tiddly-winks) that we call ‘a game’ is something that is played. But in neither case is what is speciﬁed something that enables us to determine whether or not something falls under the concept in question. Rather, Wittgenstein avers, truth and falsehood ‘belong’ to the concept of a proposition (as check belongs to the concept of the chess king), but do not ﬁt it.9 8

Cf. TLP 6.111, which alludes to Russell’s early view in ‘Meinong’s Theory of Complexes and Assumptions’, repr. in The Collected Papers of Bertrand Russell, vol. 4: Foundations of Logic 1903–5 (Routledge, London and New York, 1994), p. 473. Moore too had once thought that truth is a simple unanalysable property that some propositions have and others lack. The propositions that have this property, he had held, are facts, and reality consists of the totality of such propositions that have this property and their constituent concepts (Some Main Problems of Philosophy (Allen and Unwin, London, 1953), p. 261). 9 Not, perhaps, the happiest way of putting matters, since pain-behaviour ‘belongs’ to the concept of pain, but this does not mean that it is not a criterion for being in pain.

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5. Truth, correspondence and multi-valued logic Investigations §136 bluntly declares that ‘p’ is true = p

and ‘p’ is false = not-p

Exactly what Wittgenstein meant by this excessively brief and ill-formulated remark is, as we have seen, not altogether clear. But at any rate, there is no reason whatsoever for thinking that it involves any commitment to a Correspondence Theory of Truth, and every reason for thinking that it eschews any such account. The moot question is whether §136 is an innovation relative to the Tractatus? It is very tempting to pin the Correspondence Theory of Truth on the Tractatus, and to see Investigations §136 as a change of mind.10 But this would be too hasty. Already in the pre-Tractatus notebooks Wittgenstein observed that ‘ “p” is true, says nothing else but p’ (NB 9), and in his ‘Notes on Logic’ that ‘a proposition is then true when it is as we assert in this proposition’ (NB 97; cf. NB 113). In the Tractatus he observed that ‘a proposition is true if things are as we, by using it, say they are’ (TLP 4.062, modiﬁed translation). This looks very similar to Ramsey’s later account of truth — indeed, very like what Wittgenstein himself says later in the Grammar (PG 123; cf. RFM 117) and the Investigations. The question that must be examined is whether these important remarks are compatible with a Correspondence Theory of Truth. If not, did Wittgenstein inconsistently embrace a Correspondence Theory in the Tractatus? Or is it, despite appearances, a mistake to ascribe such an account to the book? Many different kinds of account of truth have invoked the notion of correspondence or agreement.11 An account of truth that merits the name ‘Correspondence Theory of Truth’ must hold that truth is not only a property but a relational property (as being married or being a spouse is a relational property). It has variously been held to be a relational property of a sentence, a proposition or a judgement. The implied relatum was conceived by classical and medieval correspondence theorists to be an object: namely, the thing which a proposition or judgement is about. The relation of correspondence

10

This was the view adopted in the ﬁrst edition of this Commentary, in the original essay ‘The general propositional form’ and the exegesis of §136. 11 For an exhaustive typology and meticulous historical investigation, to which I am indebted, see Wolfgang Künne, Conceptions of Truth (Clarendon Press, Oxford, 2003), ch. 3.

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or agreement was held to consist in the proposition’s or judgement’s ascribing to its object a property that the object actually possesses. Early twentiethcentury correspondence theorists (e.g. Moore and Russell) held the implied relatum to be a fact. The unique relation between the true belief that p and the fact that p, Moore called ‘correspondence’. However, he gave no explanation of what this relation consisted in. He wrote (in 1910): using the name ‘correspondence’ merely as a name for this relation, we can at once assert ‘To say that this belief is true is to say that there is in the Universe a fact to which it corresponds; and to say that it is false is to say that there is not in the Universe any fact to which it corresponds.’ And this statement, I think, fulﬁls all the requirements of what we actually mean by saying that the belief is true or false.12

The thought that being true is a relational property was nicely epitomized by Russell’s later remark that ‘the difference between a true belief and a false one is like that between a wife and a spinster’.13 Where, then, does the Tractatus stand on these matters? Although Wittgenstein, in his various remarks on truth cited above, seems implicitly to have denied that being true is a relational property, he also insisted that ‘A picture agrees with reality or fails to agree; it is correct or incorrect, true or false’ (TLP 2.21), that ‘The agreement or disagreement of its sense with reality constitutes its truth or falsity’ (TLP 2.222), and that ‘In order to tell whether a picture is true or false we must compare it with reality’ (TLP 2.223). These remarks may appear to suggest a commitment to a correspondence account of truth. But that would be a misunderstanding. For these passages do not claim that being true is a relational property of propositions, and do not explain the concept of truth in terms of a relation of correspondence between a proposition and a fact. Rather, they explain the concept of truth in terms of the agreement of the sense of a picture with reality. A picture represents a possible situation in logical space (TLP 2.002). What it represents is its sense (TLP 2.221). Its sense agrees with reality if the possibility depicted is realized. The truth of a proposition therefore does not consist in a relation of correspondence between a proposition and a fact (can facts be the relata of genuine binary relations in the Tractatus?), but rather in the actuality of its sense. (It is, one might be tempted to say, a form of coincidence — a coincidence of a possibility with its actualization, but, of course, that is not really a form of coincidence at all.) To ﬁnd out whether the sense is actualized or not, one must compare the proposition with reality, i.e. verify it. For one cannot tell, merely by looking at the proposition, whether things are as it depicts them as being. If Wittgenstein were committed to a correspondence account of truth, we should need to know what the relationship of correspondence between a 12 13

G. E. Moore, Some Main Problems of Philosophy (Allen and Unwin, London, 1953), pp. 276f. Russell, Human Knowledge: Its Scope and its Limits (Allen and Unwin, London, 1948), p. 165.

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proposition and the fact that makes it true consists in. The only candidate seems to be given by the notion of depicting. So we might say that the truth of a proposition is a relational property which consists in the proposition’s standing in the depicting relation to a fact. But that would be wrong, since what a proposition depicts is a state of affairs (a possibility, not an actuality), irrespective of whether it obtains or not. The pictorial relationship is the relationship between the names that are constituents of the picture and the objects that are their meanings that ensures identical logical multiplicity and isomorphism between a picture and what it represents. But what a proposition represents is a possible situation in logical space (TLP 2.202) — its sense (TLP 2.221). A proposition does not stand in a relation to its sense, which is a mere possibility — it shows its sense and says, truly or falsely, that it obtains. And it is crucial to the picture theory of representation, and to its resolution of the problems of intentionality, that the proposition depicts the very same thing no matter whether it is true or false. A further factor precluded construing being true as a relational property. A central plank of the Tractatus platform was that the logical connectives are not names of functions, properties or relations. For this purpose, Wittgenstein invented the T/F notation, which demonstrated that we can, in principle, dispense with the logical connectives altogether.14 But this argument depends on the thought that ‘true’ and ‘false’ are not themselves names of properties (let alone of relational properties). For if ‘is true’ were the name of a property (a relational property), then (to use Wittgenstein’s formulae) ‘ “p” is true’ would not be replaceable by ‘p’, nor would ‘ “p” is false’ be replaceable by ‘not-p’. Further difﬁculties turn on the ontology of the Tractatus. If being true were a property, then truth and falsehood would be objects (in the Tractatus sense of the term). But they would be objects that cannot concatenate with other objects in a possible state of affairs, but, singularly, only with facts (i.e. representing facts). But can facts combine with objects? No provision is made in the ontology of the Tractatus for any such possibility. Furthermore, if truth and falsity were ‘objects’ — namely, relational properties — they would be properties that some facts (representing facts) happen to have, and other facts lack — a supposition that Wittgenstein surely would have repudiated, inasmuch as being true or false is conceived to be part of the essence of a proposition. So truth and falsity could not possibly be conceived to be material properties of 14

In his lectures in the 1930s he remarked that discussion of ‘true’ and ‘false’ is made easier once it is realized that they can be done away with altogether: ‘Instead of saying “p is true” we shall say “p”, and instead of “p is false”, “not-p”. That is, instead of the notions of truth and falsity, we use proposition and negation.’ He then added: ‘On the other hand, we could do away with negation, disjunction, conjunction, etc. and use true and false, making up a notation containing only the words “true” and “false”. I once did that, with the notation for truth-functions [the T/F notation]. By replacing our ordinary notation by this one, what logical propositions are is made clear’ (AWL 106).

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propositions. Could they then be formal properties? Obviously not, since formal properties show themselves in the features of genuine propositions. But one thing that empirical propositions cannot be conceived to show is their own truth or falsehood — for that one must compare them with reality. So at most the ‘property’ of being-either-true-or-false might be taken to be a formal property of a proposition, but not being true or being false. Finally, there are other difﬁculties in construing ‘ “p” is true’ and ‘ “p” is false’ as predicating properties of a proposition. For if ‘ “p” is true’ says that the proposition ‘p’ stands in an appropriate correspondence relation to the fact that p, then that is obviously something that cannot be said, since both fact and proposition are formal concepts. But equally obviously, it is not something that can be shown either, for, to repeat, one cannot read off from the form of an empirical proposition ‘p’ that it is true. It is noteworthy that Wittgenstein considered the idea that ‘ “p” is true’ is a pseudo-proposition (NB 9), but there is no later trace of it. Rather than tacitly cleaving to this idea, it seems more likely that he came to think that ‘is true’ is not a name of an object (property or relation), that being true is not a genuine property at all (but more akin to adding 0, or multiplication by 1), and that this is why ‘ “p” is true = p’ (and ‘ “p” is true = “p” says that p, and p’ (cf. NB 113)). It is, of course, correct that, according to the Tractatus, every true proposition with a sense is made true by a fact. Moreover, the conception of facts advanced is substantial — the world, according to the Tractatus, consists of facts. It is also true that correspondence does come into the tale — not as a truthconstituting relation, but as part of the account of sense. For the sense of a proposition is a function of the meanings of its constituent names, and the meanings of such names are the objects (including properties and relations) in reality that correspond to (not with) them. But if we construe correspondence theories of truth as holding that being true is a relational property of sentences or propositions, then, despite these afﬁnities, the Tractatus does not propound a correspondence theory of truth. For one cannot consistently both hold that being true is a relational property and embrace the formulae ‘ “p” is true = p’ and ‘ “p” is false = not-p’. But one might well say that the metaphysics of symbolism, the picture theory of the proposition, and the ontology of the Tractatus are all in the spirit of a correspondence theory of truth. For, to be sure, according to the metaphysics of the Tractatus, for every true proposition there is some fact that corresponds to it and that makes it true. If this is a correct reconstruction of Wittgenstein’s early ideas, then it becomes clear why he could, to a large extent, retain the form of his early account of truth in his later philosophy. What he did was to sever his account of truth from its associations with the metaphysics and ontology of logical atomism and with the picture theory of the proposition. The remarks on the nature of truth could be retained. But far from constituting ineffable metalogical insights into the essential nature of representation, they were now no more than grammatical statements:

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Suppose I say that it will rain tomorrow. What is the state of affairs that is signiﬁed by this proposition? That it will rain tomorrow. That is, in reply we get the proposition itself or some synonymous transformation of the proposition. Hence this rule holds: The expression ‘the state of affairs signiﬁed by p’ can be replaced by ‘p’. If the words ‘true’ and ‘state of affairs’ are eliminated from the explanation, then the explanation reads: p if p. In fact, I have with this explanation made a contribution to the grammar of the word ‘true’. (VoW 491)15

In effect, Wittgenstein now argues, one can give a variety of paraphrases of truth-predications, all of which may, in some context or other, be appropriate. One may say that the proposition that p is true, for example, if it is the case that p, if the state of affairs that p obtains, if the proposition that p agrees with reality, if things are as the proposition that p says they are, if it is a fact that p. None of these is a metalogical statement. They are all grammatical statements, and their enumeration — the exhibition of all these complicated connections — is the explanation of truth. It is a grammatical description. And the words ‘true’ and ‘agreement’ (MS 113 (Vol. IX), 490; MS 115 (Vol. XI), 85) are not metalogical words that set up a connection between language and reality, but are ‘only words within a speciﬁc calculus of language, just like “yes” and “no” ’ (VoW 493). It is also evident, from the discussion of truth in the Grammar, that the core of the early view was retained, but cut loose from its metaphysical wrappings. There, in a passage (PG 123) that is the precursor of Investigations §136, Wittgenstein points out, as he had done in the Notebooks, that ‘ “p” is true = p’, that ‘ “p” is false = not-p’, and adds ‘What he says is true = Things are as he says’. In The Big Typescript he observed that one uses the word ‘true’ in such contexts as ‘What he said is true’, but that only says the same as ‘He says “p” and it is the case that p’ (BT 76). These are nice elaborations of the Tractatus claim of 4.062: ‘a proposition is true if things are as we, by using it, say they are’.16 But by now the commitment to the ontology of facts and states of affairs, and the adherence to the picture theory of representation, had been abandoned. He did not, however, think that this was the end of the matter, not because there was a metaphysical hinterland behind the account of truth, as he had supposed when writing the Tractatus, but because the equivalence gives only a small part of the grammar of ‘true’. 15

This is very poorly expressed, although some of the unclarity may be due to the fact that Waismann was taking a dictation. Punctuation apart (viz. ‘the state of affairs signiﬁed by “p” ’), the expression ‘the state of affairs signiﬁed by “p” ’ is (a stand-in for) a singular term, whereas ‘p’ is (a stand-in for) a sentence. So more precision is called for. Nevertheless, Wittgenstein’s point is reasonably clear. The explanation ‘the proposition that p is true if and only if the state of affairs that p obtains’ amounts to no more than a fancy way of saying that p if and only if p, which exploits the grammatical connection between the two singular terms ‘the proposition that p’ and ‘the proposition made true by the obtaining of the state of affairs that p’. 16 See also NB 97 and NB 113: ‘ “p” is true = “p” . p . Def.: only instead of “p” we must here introduce the general form of a proposition.’

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Since the concept of a proposition is a family-resemblance one, what it is for one kind of proposition to be true may be very different from what it is for another to be true, and some of the licit paraphrases apply readily to some kinds of proposition and not to others. To say that an empirical proposition such as ‘It is raining’ is true is tantamount to saying that things are as it describes them as being, or that it is a fact that it is raining. But to say that it is true that 25 × 25 = 625 is not to say that things are as that proposition describes them as being, or that the state of affairs that 25 × 25 = 625 obtains or that it is a fact that 25 × 25 = 625. For the proposition ‘25 × 25 = 625’ is not a description of any kind, that 25 × 25 = 625 is not a state of affairs that might or might not obtain, and it is not a fact (a matter of fact, something that could be otherwise) that 25 × 25 = 625. Rather, to say that this proposition is true is to say that it is a proposition of mathematics, a rule for the transformation of empirical propositions concerning magnitudes and quantities, etc. Truth and falsehood in arithmetic correspond to sense and nonsense among empirical propositions (MS 163, 47v–r; for discussion, see Volume 2, ‘Grammar and necessity’, sect. 3), that is: a true arithmetical proposition corresponds to a valid (sensible) piece of reasoning among empirical propositions (‘I have 2 pennies in my left hand and 2 pennies in my right hand, so I have 4 pennies in both hands’), and a false one to an invalid (nonsensical) transition between propositions (‘I have 2 pennies in one hand and 2 pennies in the other, so I have 22 pennies’). Similarly, to say that a proposition of logic in the propositional calculus is true is not to say that things are as it describes them as being, but rather to say that it is a tautology. ‘It is true that . . .’ and ‘is true’ are not ambiguous, but what these expressions operate on or are predicated of may differ fundamentally from one domain to another. For the concept of a proposition is a family-resemblance one, and what a truth-operation or truthpredication amounts to may differ from one member of the family to another (the family including, for example, perceptual, theoretical, arithmetical, logical, ethical, religious propositions). What kind of thing one afﬁrms or reafﬁrms by the use of the truth-operator or truth-predication with respect to the assertion of a proposition of a given type (e.g. the obtaining of an empirical state of affairs, the existence of a rule, the endorsement of a value) depends on the nature of the proposition-type operated on or the subject of the predication. We have noted that while Wittgenstein qualiﬁed his earlier insistence that every proposition must be bipolar, he continued to cleave to the requirement of bivalency. (He had, as far as I know, nothing to say concerning truth-value gaps, about which debate erupted in the 1950s apropos Strawson’s criticisms of Russell’s Theory of Descriptions.) He explicitly denied that Brouwer had discovered propositions of arithmetic that lack a truth-value. Rather, he said, Brouwer had discovered structures that looked like propositions but were not (AWL 140). What view did he take of alternative logics that admit more than two truth-values, such as Lukasiewicz’s? There is an aside on the matter in his Cambridge lectures (AWL 139) and a more detailed discussion in the Principles (PLP 27–34), which may derive from a lost dictation.

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Lukasiewicz’s three-valued logic stemmed from reﬂections on future contingencies. In his view, propositions concerning the future, e.g. ‘There will be a sea battle tomorrow’, are neither true nor false now (at the time of utterance) and must be assigned a third truth-value, viz. possible. In the calculus Lukasiewicz developed, future-tensed propositions are neither true (1) nor false (0) but undecided ( 1/2). Wittgenstein’s response was to challenge the reasoning that led to the construction of the three-valued calculus. The idea that a future-tensed proposition is neither true nor false now is more problematic than it seems. What exactly is Lukasiewicz denying? What is meant by saying that a proposition about the future is already true or false now? If it is accepted that ‘It is true that p’ says neither more nor less than ‘p’ and that ‘It is false that p’ = ‘~p’, then ‘That p is true now’ is equivalent to ‘p now’, and ‘That p is false now’ to ‘~p now’. If ‘p’ is ‘There will be a sea battle tomorrow’, then ‘That p is (already) true now’ = ‘There will be a sea battle tomorrow (already) now’, which is nonsense, and ‘That p is (already) false now’ = ‘There will not be a sea battle tomorrow (already) now’, which is also nonsense.17 So we cannot say, as Lukasiewicz suggests, that it is neither true nor false now that there will be a sea battle tomorrow, and that the law of excluded middle does not apply to such propositions, for they are not propositions. Rather, we should conclude that the question of whether a future-tensed proposition is or is not already true now is nonsense (but, of course, it may well be true that there will be a sea battle tomorrow, and it may well be true to say now that there will be one tomorrow). It is a nonsense that stems in part from the thought that saying that a proposition is true is ascribing a property to it such that it makes sense to ask when it has that property.18 There is nothing wrong with Lukasiewicz’s three-valued calculus. But it is not a correct representation of our concepts of proposition, truth and falsehood, and not an alternative form of representation of the logic of our language to our two-valued logic. It is a new game, but not an extension of logic representing a discovery about the nature of propositions (AWL 139).

17

Of course, there is a use for ‘Now it will be the case that p’: namely, if it has been decided to bring it about that p and the possibility that not-p has been blocked. Furthermore, there is a use for ‘Now it is true that it will be the case that p’. For example, if someone has asserted that it is false that there will be a sea battle tomorrow, one might take action to ensure the clash of ﬂeets, and triumphantly assert in the face of the previous denial ‘Now it is true that there will be a battle tomorrow’. 18 To be sure, Wittgenstein (or Waismann) fails to attend to perfectly respectable assertions such as ‘It used to be true that London was larger than Beijing, but it no longer is’. All it means is that London used to be larger than Beijing and no longer is. Of course, this does mean that one can ask whether it is now true (whether it was true, and whether it will be true) that London is . . . But the temporal index, despite appearances, qualiﬁes the possession of the property that is being ascribed.

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

XVII

Understanding and ability 1. The place of the elucidation of understanding in the Investigations §§1–142 of the Investigations are Janus-faced, looking back to the errors of the Tractatus (conceived to exemplify a way of thinking that characterizes a major strand in the philosophical tradition) and forward to the very different account now being unfolded. The Augustinian conception of meaning has been subjected to criticism, and the conception of the meaning of a word as its use has been proposed. Ostensive explanation, understood as linking language and reality, has been criticized, and a quite different idea of ostensive deﬁnition as ‘remaining within language’ has been defended. Atomism has been criticized, and analysis on the atomist model rejected. Essentialism and real deﬁnition have been repudiated, the quest for analytic deﬁnitions has been reduced to its proper proportions, the conception of family resemblance has been introduced and clariﬁed, and the demand for determinacy of sense abandoned. The metaphysical impulse has been curbed, and the sublime conception of philosophy rejected and replaced by a quite different understanding of the subject as therapeutic and elucidatory. The quest for the general propositional form has been declared chimerical, since the concept of a proposition is a family-resemblance one. §§138– 42 mark a change. While still looking back to the Tractatus, these sections introduce a problem raised by the new conception of language and linguistic meaning, and the discussion thenceforth moves off in fresh directions. The meaning of an expression is its use. The use of an expression is something exhibited over time, in the manifold applications of the expression in all the variety of contexts in which it can legitimately occur. But one normally understands an expression at a stroke. Someone utters a word or sentence. Straightaway we understand what he has said and the meanings of the words he has used. How can that be? How can one grasp in an instant something that is thus ‘spread out over time’ (PI §139)? How can what we thus grasp — i.e. the meaning that we understand at a stroke — ﬁt the complex use of the expression? What is it that we grasp instantaneously, that enables us to act appropriately? We grasp the meaning of the words uttered and understand what is meant by the sentence in which they occur. But if the meaning of the words is their use, how can that be grasped in an instant? We have already learnt that we should not conceive of the use of an expression as something that

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follows from the meaning (the meaning-body conception that Wittgenstein has rejected), but now the phenomena of understanding seem to push us inexorably back into this misconception — ‘It can’t be like that, and yet it must be like that!’ is what we seem forced to say. When we understand an expression that is explained to us, what happens that enables us to go on and use the expression correctly? For, to be sure, the speciﬁc uses we make of the expression are not the understanding. They are exempliﬁcations of understanding. Do we not use the expression thus precisely because we understand it? Similarly, if we are presented with a fragment of an algebraic series, we may suddenly ‘see’ the rule in the series, suddenly understand the principle of the series, and go on to develop the series correctly. But our further expansion of the series is not what our understanding consists in. It is something that ﬂows from our understanding. So, we are tempted to think that our understanding must consist of something’s being before our mind that enables us to go on to do those things that exhibit understanding. We might think that understanding must consist in having a mental picture or an idea before our mind’s eye, as the empiricists held. Or we might think that understanding consists in the rule for the use of the expression occurring to us ( just as we might think that knowing how to continue a series consists in the rule for the series occurring to us). But the operative rule for the use of a word (or for a series) may come to mind, and yet one may nevertheless misapply the word for which it is the explanation (or develop the series wrongly). Now it seems that understanding must consist in a special mental act, process or activity. Frege held that understanding the sense of a sentence as used on an occasion is a special mental act or process of grasping the thought expressed (PW 145). The empiricists held that understanding involves a process of association. For the meaning of a word was conceived to be the idea with which it is associated and for which it stands. Understanding the words of another was held to be a matter of associating the same ideas as he with the words he utters, and apprehending the judgement he expressed by his utterance (i.e. that such-and-such an idea is afﬁrmed or denied of another). Modern philosophers and linguists are inclined to think of understanding as an activity of interpreting the words heard. This conception dominated late twentiethcentury reﬂections on language by philosophers and linguists, who held that we derive the meaning of a sentence from the meanings of the words thus interpreted and their mode of combination. For we can understand sentences we have never heard before, and this seemed to require a computational process of interpretation (see ‘Contextual dicta and contextual principles’, sect. 6). Our understanding of the words of which sentences are composed was thought to consist of tacit knowledge of the meaning-axioms of a theory of meaning. But if having the rule for the use of a word explicitly in mind is compatible with misapplying the word, surely having it implicitly in mind, ‘buried deep in the unconscious’ (as Chomsky argued), is too. Do we derive the meaning of the sentences we hear from these ‘unconscious’ rules? Is that the process of understanding? Since we can discern no conscious mental ideas, representations or

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meaning-axioms and no conscious processes of derivation, interpretation or computation, we postulate unconscious ones, also ‘buried deep in the unconscious mind’. But that seems incompatible with the idea of being guided by a rule, of using a rule as a standard of correctness, and of a rule’s affording a reason for acting in a certain way. So we may now suppose that understanding consists in a neural state that disposes us to behave in such a manner that exhibits understanding. Accordingly, understanding is not a mental state, but a dispositional state of the brain (cf. Exg. §149). So one putative theory succeeds another, although none is open to empirical conﬁrmation. Each mesmerizes us for a while, until it is displaced by the next. To dissolve these puzzles, a clariﬁcation of the concept of understanding is required. For if the concept of understanding is misconstrued, then the concept of meaning (Bedeutung) that is its correlate will be too, and so will the concepts of meaning something (meinen) by one’s words and of what is said and what is meant by an utterance. The purpose of Wittgenstein’s long examination of understanding in §§143–84 is to take the ﬁrst steps towards such clariﬁcation. This discussion also prepares the ground for the subsequent elucidation of what it is for something to follow from a rule (and from an explanation of meaning), and what it is for someone to follow a rule (and to apply a word in accordance with the rules for its use). The corresponding examination of meaning something (meinen) is, rather curiously, deferred until §§661–93 at the very end of the book (see Volume 4, ‘The mythology of meaning something’).

2. Meaning and understanding as the soul of signs As we have seen, the meaning of an expression, with appropriate qualiﬁcations, can be said to be its use. The meaning of an expression in use is what is understood when one understands or knows what the expression, thus used, means. That, normally, is what the speaker means by uttering the words he uses. Mutatis mutandis by the word ‘W’ he means W, and by the sentence ‘p’ that he utters he means that p (with appropriate adjustments for indexicality and ambiguity). Meaning something by a word or sentence seems to be a mental act or activity that projects a sign on to whatever it signiﬁes. Understanding, in the case of a hearer, seems to be a correlative process. The speaker projects the signs on to the items he means, and the hearer, if he is to understand the utterance, must interpret the signs appropriately; i.e. he must assign the same meanings to them as the speaker has done. Then he will know what the speaker meant. So it may seem that meaning something by signs, on the one hand, and understanding what is meant by signs, on the other, are the mental processes underlying the use of signs. It is they that give life to signs.1 1

That the Tractatus cleaved to such a conception of speaker’s meaning has already been argued. It was silent on the subject of understanding. But it is plausible to suppose that correlative to the conception of speaker’s meaning as animating signs, Wittgenstein was implicitly committed to a corresponding conception of understanding as interpreting signs.

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It seems that there are certain deﬁnite mental processes bound up with the working of language, processes through which alone language can function. I mean the processes of understanding and meaning. The signs of our language seem dead without these mental processes . . . We are tempted to think that the action of language consists of two parts; an inorganic part, the handling of signs, and an organic part, which we may call understanding these signs, meaning them, interpreting them, thinking. These latter activities seem to take place in a queer kind of medium, the mind; and the mechanism of the mind, the nature of which, it seems, we don’t quite understand, can bring about effects which no material mechanism could. (BB 3.)

The idea is natural and widespread. This picture is reinforced by obvious reﬂections. Signs are arbitrary and conventional. Replacing ‘p’ by ‘t’ in ‘chap’ produces a sign with a quite different meaning, but it is arbitrary that we should employ one sign to signify thus and the other to signify otherwise. Again, ‘chat’ in English has one meaning, in French another — but the signs alone, the marks upon the paper, are quite dead. What gives them meaning, it seems, is what goes on in the mind when they are uttered or heard. It is our meaning and understanding them which gives them life. When one does not understand a sentence, nothing is missing with respect to the sign; one has the sign, what is lacking is the understanding that must accompany it, and which is its mental correlate. Similarly, when a parrot squawks an English sentence, perhaps even on an appropriate occasion, we do not say that it can speak English, for it neither means nor understands what it says. A person typically knows what he means to say before he says it. But one does not parade the words in one’s mind before putting them on public display. On the contrary, one uses the words in order to convey one’s meaning to another, to bring before his mind what is already before one’s own. Signs, it seems, are the public code for the communication of thoughts. The most noble and proﬁtable invention of all other was that of SPEECH, consisting of names or appellations, and their connection; whereby men register their thoughts; recall them when they are past; and also declare them to one another for mutual utility and conversation . . . The general use of speech is to transfer our mental discourse into verbal; or the train of our thoughts, into a train of words.2

These elementary observations incline us to think of meaning something and understanding as mental phenomena, forms of thinking (generically conceived).3 This idea is reinforced by further considerations. First, it seems that one cannot observe the understanding of another, but only the behaviour that manifests it. If one orders another to do something, one 2

Hobbes, Leviathan, ch. IV. It is noteworthy that Wittgenstein, especially in his early and middle periods, often uses the verb ‘to think’ in this generic sense, and sometimes takes it for granted that meaning something is a form of thinking.

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can observe his compliance, but not his understanding of the order, which seems a prerequisite for his compliance. Since he may understand without complying, it seems to follow that the behaviour is one thing, the understanding another. Understanding is then conceived as the underlying mental phenomenon of which the behaviour is a symptom. Indeed, we may think that only the subject of understanding really knows whether he understands. For our ‘access’ to his understanding seems to be only by inductive or analogical inference, whereas he has direct (privileged) access to his own mental life. Secondly, we are familiar with the experience of suddenly understanding something (e.g. suddenly seeing that the rule of the series 1, 5, 11, 19, 29 . . . is given by ‘an = n2 + n − 1’). We naturally speak here of a ‘ﬂash of understanding’, and readily employ metaphors of ‘mental illumination’ to describe the distinctive experience. Thirdly, when, in such cases, we exclaim ‘Now I understand!’, we do so because we understand. We do not declare our understanding on the basis of observation of our behaviour. Yet, it seems, we typically know that we understand. It is tempting to suppose that we know this in virtue of having the experience that is characteristic of understanding something. So it seems that our exclamation is a consequence, or even a report, of a mental phenomenon: namely, an act or process of understanding. Fourthly, the experiential difference between understanding and not understanding something that is temporally extended (e.g. a lecture or a piece of music) is distinctive. Listening to a lecture one does not understand, overhearing a conversation in a foreign language one does not know or knows only imperfectly, involve a very different succession of experiences from following a lecture or conversation one does understand. For someone accustomed to classical music, the experience of listening to Stockhausen is distinctive; he feels that he cannot follow the music. Understanding, it seems, is a mental phenomenon that accompanies the hearing. Likewise, when one reads an obscure text parrot-wise, what is lacking is the accompanying mental phenomenon of understanding — or so it seems. Having used a pronoun to refer to a person, one may clarify the reference by saying, ‘I meant A’. Similarly, one may assure someone that his remark is clear by saying, ‘Yes, I understood you’. The past tense of these verbs suggest that one is reporting speciﬁc past actions, like ‘I pointed at A’, or ‘I touched you’, only mental rather than physical ones. Similarly, the exclamation ‘Now I understand!’ looks like a report on a mental occurrence, akin to telling the doctor who is testing one’s movements ‘Now it hurts’. These simple considerations induce us to think of understanding (or of meaning something) as a psychological phenomenon, and invite reﬂection on what kind of phenomenon understanding must be. Is it a mental act or occurrence, or a mental state, or a process or activity, or a disposition of the mind? Various, more sophisticated reasons incline us to one or another of these options.

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3. Categorial misconceptions of understanding When we attempt to classify understanding or meaning, we ﬁnd that we are tempted in different directions. On the one hand, understanding seems to be a distinctive experience. When we understand something, in particular when we understand the speech of another, something happens, something that does not happen when we hear another speak in a language we cannot understand. That understanding is an experience seems particularly evident from the phenomena of suddenly understanding something, or of seeing the multiple aspects of something (e.g. Jastrow’s duck-rabbit, or the ambiguity of a pun). Like James, we might ask ourselves: ‘What is that ﬁrst instantaneous glimpse of someone’s meaning which we have, when in vulgar phrase we say we “twig” it? Surely an altogether speciﬁc affection of our mind.’4 It seems that it is sometimes an action, something one can try to do, and that one often succeeds in doing. But sometimes understanding seems to be a passion, something that happens to us, something that we experience. Understanding the words of another is not a voluntary action we perform and which we might refrain from performing. Rather, we hear his words and straightaway understand what he is saying. So is understanding here not an experience? Is it not precisely because this experience occurs that we can so conﬁdently say that we have understood? If understanding were not an experience, how could we explain that a person can typically say whether he understands something (even though he occasionally errs)? However, there is an equally strong temptation to conceive of understanding as a process or activity which goes on in time. Understanding readily appears to be a complex mental process that accompanies listening to the speech of others with understanding (VoW 441). James wrote: I believe that in all cases where the words are understood, the total idea may be and usually is present not only before and after the phrase has been spoken, but also whilst each word is uttered. It is the overtone, halo, or fringe of the word, as spoken in that sentence. It is never absent; no word in an understood sentence comes to consciousness as a mere noise. We feel its meaning as it passes.5

This conception is reinforced by reﬂecting upon the way one follows a speech, lecture or piece of music with understanding, which seems to accompany the aural stimuli step by step, sometimes faltering or stumbling, sometimes anticipating what is yet to come. It is this process or activity, we think, that is so obviously missing when we listen without understanding. Furthermore, sophisticated theoretical reﬂections on meaning and understanding, as noted, suggest that understanding must be a computational process of some kind. 4 5

W. James, The Principles of Psychology (Holt, New York, 1890), vol. i, p. 253. Ibid., p. 281.

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Otherwise it seems that it would be impossible to explain how we can understand sentences we have never heard before. Of course, it proves very difﬁcult to capture the speciﬁc quality of the mental experience or process which ‘understanding’ apparently names. The experiences accompanying understanding seem diverse and differ from one occasion to another. Do they have a common essence? It is difﬁcult to say. Our ﬁrst inclination is to suggest that these mental phenomena are only imperfectly accessible to introspection, for they are too quick to be captured by the eye of the mind (like the racing needle of a sewing machine). Let anyone try to cut a thought across in the middle and get a look at its section, and he will see how difﬁcult the introspective observation . . . is. The rush of thought is so headlong that it almost always brings us up at the conclusion before we can arrest it. Or if our purpose is nimble enough and we do arrest it, it ceases forthwith to be itself . . . the attempt at introspective analysis in these cases is in fact like seizing a spinning top.6

However, if we convince ourselves that at least in some cases we can slow things down to an introspectively perceptible speed, we may then be prone to complain, as James did, that ‘our psychological vocabulary is wholly inadequate to name the differences that exist’.7 So the speciﬁc process of understanding is indescribable, but nevertheless, quite particular — it is something with which each of us is intimately acquainted, even if we cannot describe it. Alternatively, we may suppose that the process of understanding is not conscious at all, and that is why we have such great difﬁculties when called upon to describe what understanding consists in. Understanding is a process of the mind all right, but an unconscious one. We shall examine that option in a moment. Nevertheless, other factors, conﬂicting with the foregoing data, point to understanding’s being a state of the mind rather than an experience, process or activity of the mind. The manifestations of understanding are a ﬁnite array of performances, but a word, which one understands, has an indeﬁnitely large range of combinatorial possibilities and applications, some of which one may never utilize. (Similarly, a rule for the expansion of a series of numbers has an inﬁnite range of applications, not all of which can be manifested in a person’s behaviour, even though we say that he has grasped the rule of the series.) What enables one to use a word correctly, just as what enables one to develop an algebraic series, is precisely that one understands the word, as one understands the principle of the series (has grasped the rule of the series). One’s correct applications of a word in any of the many contexts in which it can occur, like one’s expansions of a series, are applications of one’s understanding. After all, is understanding not closely related to knowing? And are not the speciﬁc actions that show that I know something consequences of my knowledge? And is not knowing a mental state? 6 7

Ibid., p. 244. Ibid., p. 251.

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These primitive reﬂections may be strengthened by more sophisticated considerations. Grammarians distinguish between dynamic and static (or stative) verbs.8 Dynamic verbs are held to refer to activities, processes and events. Static verbs are commonly held to ‘refer to a state of affairs, rather than to an action, event or process’,9 and to distinguish states from activities.10 It is tempting to treat this (largely syntactical) distinction between kinds of verbs as an ontological distinction,11 conceiving of a state, activity or performance as what corresponds, respectively, to a static verb, activity-verb or performance-verb. A state is then conceived as the correlate of the general form of static verbs ( just as, in Frege’s view, an object is whatever is designated by a singular referring expression). This class of verbs is characterized in terms of (i) (ii)

lack of a progressive aspect (continuous tense) lack of an imperative mood.

Other supplementary criteria are also cited by some authors. Static verbs (iii) (iv) (v) (vi)

cannot form a pseudo-cleft sentence with a Do pro-form (i.e. ‘what I did was to V . . .’) the present tense is not frequentative ‘A has V-ed’ implies ‘A Vs’ static verbs cannot be qualiﬁed by manner adverbs such as ‘quickly’, ‘slowly’, ‘reluctantly’.

So, one may understand or know, but one cannot, in the same sense, be understanding or knowing. Similarly, one can order someone to try to understand something or to learn something, but one cannot order someone to understand something he does not understand, any more than one can order someone to know (as opposed to ordering him to learn or ﬁnd out) something he does not know. ‘What I did was to understand (to know) . . .’ is awry; ‘I understand (know)’ is not frequentative, and ‘A has understood’ does indeed imply ‘A understands’ (although ‘A has known’ does not imply ‘A knows’). One cannot know something quickly, slowly or reluctantly, although it may take little or much time for someone to come to know or to learn something. And although we may say that A understood what B had in mind very quickly or 8 R. Quirk, S. Greenbaum, G. Leech and J. Svartvik, A Grammar of Contemporary English (Longman, London, 1974), pp. 39f, 92ff. 9 J. Lyons, Introduction to Theoretical Linguistics (Cambridge University Press, Cambridge, 1968), p. 315. 10 Ibid., p. 316; cf. F. R. Palmer, The English Verb (Longman, London, 1974), pp. 70ff. Palmer subdivides non-progressive verbs into (i) private verbs: ‘those that refer to states or activities that the speaker alone is aware of ’ and (ii) verbs of state: ‘which refer not to an activity but to a state or condition’. 11 See A. J. P. Kenny, Action, Emotion and the Will (Routledge and Kegan Paul, London, 1963), pp. 171ff.

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took ages to understand the plan B was proposing, what that means is that it took little or much time for him to come to understand the plan. So it seems that to understand is indeed a state of the mind or mental state (‘Zustand der Seele’ (PI §149) or ‘seelischer Zustand’ (PI p. 59/50n. (a))). What can be said about this alleged state of mind? Restricting consideration to understanding the meaning of an expression, there are various options that have been tried. The classical empiricist conception was to take understanding the meaning of a word one hears or utters as a matter of being in a mental state that consists in having an idea or mental image before one’s mind. Behaviour that exhibits understanding is then conceived to be a consequence of having the appropriate image. For example, if one is ordered to bring a yellow ﬂower, and one understands the order, one will have an image of yellow before one’s mind, and it is this that explains why one picks a daffodil, for example, rather than a poppy. But one might eschew the imagist (idealist) conception of linguistic meaning and understanding, and hold that the mental state of understanding consists in having the rule for the use of the expression in mind, just as one might think that understanding or knowing how to continue a series consists in having the rule of the series before one’s mind. Then, it seems, the mental state explains how it is that one can go on to use the expression or to develop the series correctly. Understanding is a speciﬁc state of mind from which the performances manifesting it ﬂow, like water from a reservoir (BB 143). However, it is, at the very least, implausible to suppose that understanding the speech of another involves apprehending a kaleidoscope of mental images corresponding to the words one understands. And it is equally implausible to suppose that one thinks of the rules for the use of the words one uses correctly whenever one speaks, or hears something said, with understanding. In response to such qualms, it may seem tempting to agree that understanding is a state all right, only not a conscious one. It is a hypothesized state of an apparatus of the mind — an apparatus that subserves the mind and explains the mental acts and activities of the mind that are conscious as well as the forms of behaviour that exhibit understanding (PI §149 and Exg.). Two options dominate reﬂections: the apparatus may be conceived to be a mechanism of a postulated mind-model, or it may be conceived to be the brain. The former option is exhibited in reﬂections of the most inﬂuential linguistic theorist of the twentieth century, Noam Chomsky: . . . it is hard to see how one can seriously doubt . . . that language is both used and learned in accordance with strict principles of mental organization, largely inaccessible to introspection, but in principle at least, open to investigation in more indirect ways.12 12

N. Chomsky, ‘Some Empirical Assumptions in Modern Philosophy of Language’, in Philosophy, Science and Method: Essays in Honour of Ernest Nagel, ed. S. Morgenbesser, P. Suppes and M. White (St Martin’s Press, New York, 1969), p. 277.

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Since the correlation between mind and brain is (on this view) as yet imperfectly understood, the most we can do for the moment is try to develop an abstract structural model of such a hypothesized mental organization. It seems to me that the most hopeful approach to-day is to describe the phenomena of language and of mental activity as accurately as possible, to try to develop an abstract theoretical apparatus that will, as far as possible, account for these phenomena and reveal the principles of their organization and functioning, without attempting, for the present, to relate the postulated mental structures and processes to any physiological mechanism or to interpret mental functions in terms of ‘physical causes’.13

One of the many difﬁculties of this idea consists in the notion of mental structures. Not all structures need to be literally embodied. We speak freely of logical or mathematical structures. But just because of this, the ‘structures’ we have in mind are those of a calculus, a set of formal relations constituted by rules for the use of a symbolism. To be sure, we speak of the structure of a sonnet or a novel, but here there is no question of the structures being embodied in anything other than the writings of which they are the structure. In such contexts it makes no sense to suppose that anything is ‘hidden’, awaiting future scientiﬁc discovery. The obvious danger of talking of mental structures is the misguided temptation to think of the mind as a mysterious, imperfectly understood medium. If overt behaviour is merely empirical evidence for as yet inaccessible and unknown mental mechanisms, it will be entirely natural to wonder what these are. Then Wittgenstein’s failure to construct hypotheses about these inner structures will seem bizarre. One will be struck by the curious, and I believe stultifying, decisions to concentrate on evidence . . . putting aside the question of what the evidence is evidence for. The traditional answer to this question was that the observed phenomena are evidence for an underlying mental reality.14

But, of course, the traditional answer conceived of the ‘underlying mental reality’ as a peculiar type of substance, standing in contrast to material substance, but none the less substance for all its mentality. Indeed, James (unlike Descartes) at one point suggests ‘The consciousness of the “idea” and that of the words are thus consubstantial. They are made of the same “mind-stuff ”, and form an unbroken stream.’15 Consequently, the structure of the mind thus conceived may be taken to be the structure of such an aethereal (and mysterious) mental stuff. But if this absurdity is avoided, then the concept of structure boils down to no more than the conceptual relations between the elements of the 13

N. Chomsky, Language and Mind (Harcourt, Brace and World, New York, 1968), p. 12. Chomsky, ‘Some Empirical Assumptions in Modern Philosophy of Language’, p. 281. (This is part of his criticism of Wittgenstein’s ‘behaviourism’.) 15 James, Principles of Psychology, vol. i, pp. 281f. 14

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theory that is being invoked. So not only is the structure not hidden, but it is a feature of the form of representation, not of what is represented. The alternative to states postulated by an abstract mind-model is to suppose that understanding is a neural state of some as yet unknown kind. Central State Materialism explicitly construed mental states, processes and experiences as states of a person ‘apt for bringing about a certain sort of behaviour’.16 Such states ‘actually stand behind their manifestations’, and are conceived of as causally responsible for the behaviour that manifests them. Thus, the behaviour that we identify as a manifestation of meaning and understanding is indeed a symptom of the ‘underlying mental reality’. However, unlike the classical dualist conception of the mind, the Central State Materialist contended that It may now be asserted that, once it be granted that the concept of a mental state is the concept of a state of a person apt for the production of certain sorts of behaviour, the identiﬁcation of these states with physico-chemical states of the brain is, in the present state of knowledge, nearly as good a bet as the identiﬁcation of the gene with the DNA molecule.17

Nor is it only philosophers who are inclined to think that what is obscure about meaning and understanding will be ﬁnally clariﬁed only by neurophysiology. The idea penetrates linguistics and psychology: Whatever it is that represents . . . past and future or imagined events in our mind is the main part, if not the whole, of reality as we grasp it. The link to meaning is there — beyond the reach of any instruments we now have. As one team of psychologists sees it, meaning is the part of language that is least understood ‘because in all probability it reﬂects the principles of neural organization in the cerebral hemisphere’.18

4. Categorial clariﬁcation All these misconceptions are assailed in Wittgenstein’s writings. In various ways they transgress the grammar of ‘understand’, allocating the concept to the wrong category. The ﬁrst step towards wisdom is to attain a distinct idea of understanding, to rectify its miscategorization and the associated confusions. Understanding is neither an experience nor a mental process or act. It is not a mental state. It is not a hypothetical state of a mind-model. And it is not a dispositional state of the brain either. 16

See e.g. D. M. Armstrong, A Materialist Theory of the Mind (Routledge and Kegan Paul, London, 1968), pp. 82ff. 17 Ibid., p. 90. 18 D. Bolinger, Aspects of Language, 2nd edn (Harcourt, Brace, Jovanovich, New York, 1975), p. 187 (quoting S. Locke, D. Caplan and L. Kellar, A Study in Neurolinguistics (Charles C. Thomas, Springﬁeld, ill., 1973), p. 10).

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(a) Understanding is not an experience Contrary to what is suggested by some of the phenomena of understanding, understanding is not an experience. Of course, there is such a thing as the experience of suddenly understanding — an ‘Aha-Erlebnis’ as the Germans say. The experience, however, is not the understanding, but an accompaniment of it, and a description of the experience is not a description of understanding. What happens when one suddenly understands? Many things may happen: one may have various mental images, say certain things to oneself, experience a certain tensing or relaxing of the muscles — or one may not. When one suddenly grasps the rule of a series, one may exclaim ‘Now I can go on!’, one’s face may light up, and the rhythm of one’s breathing may change. But one may have all these experiences and yet not understand (PI §§151ff.). And conversely, if asked, ‘What happened when you understood the rule of the series?’, one may answer blankly, ‘Well, I continued the series. Nothing else happened.’ The experiences are neither necessary nor sufﬁcient for understanding. The criteria for understanding lie in performances, not in experiences. Other things being equal, the pupil can be said to understand the rule of the series when he goes on to expand the series correctly. Of course, often prior to going on to expand a series according to a rule, the thought of the rule of the series may occur to one. But ‘Now I can go on!’ does not mean ‘The formula has occurred to me’ (PI §152; BB 113). Nor does one exclaim ‘Now I understand!’ because the formula has occurred to one and one has inductively correlated past realizations of the formula with successful applications (PI §147). The formula may indeed cross one’s mind, yet one may not understand. To be sure, there is a connection between the formula’s occurring to one and going on correctly. The pupil rightly uses the words ‘Now I understand!’ when the formula occurs to him, given the circumstances that he has learnt algebra, expanded such series before, etc. (PI §154). But the words are not a description of these circumstances. We persist in thinking that when we say ‘Now I understand!’, we say so because we understand, and therefore our words are a report of an ‘introspectible experience’. This is mistaken, even if there is an appropriate experience. We should rather consider the exclamation to be a signal of understanding (PI §§180, 323), which is judged to be correctly employed by what the pupil goes on to do (although, in special circumstances, it may have been correctly used even though, when the pupil tried to do what he said he could do, he could not (PI §§181f.)). Although the speaker enjoys no special authority regarding whether he understands, his exclamation of understanding is not a mere symptom of understanding. The empiricist conception, according to which understanding the meaning of a word is having a mental image of what it signiﬁes, is mistaken. It may be that when one orders a person to pick a yellow marble from a collection, if he understands the order, he has an image of yellow. But his

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understanding does not consist in his having such an image. The temptation to think it does is lessened by reﬂecting on the order ‘Imagine a yellow patch!’ (BB 12). For surely it is not necessary for him to imagine a yellow patch in order to understand the order, and then imagine another yellow patch in order to obey it? A yellow piece of paper in one’s pocket is no less serviceable than an image of yellow in one’s mind. Indeed, it is more serviceable, since one can look at it in different lights, hold it up next to other objects for match or mismatch; i.e. unlike a mental image it can function as a genuine sample. Of course, one may forget what colour the piece of paper is (namely, that it is (called) yellow). But one may equally forget what colour one’s mental image is an image of. The criteria for having a mental image differ from the criteria for understanding. A sincere avowal concerning one’s mental imagery is authoritative, but a sincere avowal concerning one’s understanding is not. It may be undermined by one’s subsequent behaviour, if the latter manifests misunderstanding. The criteria for having images presuppose the criteria for understanding inasmuch as a person, when asked what images he has, must understand the question (hence satisfy the criteria for understanding) and the words he uses to answer it. The grammars of ‘understanding’ and of ‘having an image before one’s mind’ are totally different. We do not deny that a person understands a sentence because he cannot draw a sketch from it. Why should we suppose that he must draw a mental sketch (PI §396)? The idea that understanding an expression consists in the rule for its use occurring to one is a non-starter. It is obvious that when we speak, we do not rehearse, sotto voce, the rules for the use of the words we are about to utter. We would not deny understanding to a person who insisted that no rule occurred to him when he used an expression. Nor would we grant that a person understood an expression if he misapplied it but told us that the deﬁnition of the word did occur to him. It is equally obvious that when we hear the speech of another with understanding, we do not engage in any overt derivations or calculations in accordance with rules. That is not how rules ‘enter into’ the practice of using language. So this picture of linguistic understanding is immediately driven underground, as it were. Any rules must be deeply buried beyond the reach of the conscious mind, and any derivations, calculations or computations must take place as quickly as a ﬂash in the unconscious mind. We shall examine this supposition below. (b) Understanding is not a process However, if understanding is not an experience, neither is it an activity or process in the mind. To call understanding a process is as misleading as calling the number three an object (PG 85). Processes take time (go on). They consist of a sequence of events or actions, which may be repetitive or may not. If not, they may consist of various ordered phases. They are clockable. They can

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be interrupted, and sometimes later resumed. Wittgenstein does not deny that there are mental processes. Humming a tune, reciting poetry, or saying the alphabet in one’s imagination or silently counting one’s steps are mental processes. But understanding is not. It is true that when one listens to a lecture or watches a game of chess with understanding, one has a distinctive succession of experiences, different from those which accompany uncomprehending attention. But the experiences vary from case to case, as well as from person to person, and are not characteristic marks of understanding. Moreover, even if perchance the process, the sequence of experiences, were characteristic, it would not constitute understanding, for we do not determine whether someone understands by discovering what processes accompanied his listening. No accompanying mental process is either necessary or sufﬁcient for understanding. Whether a person understands a lecture is determined by whether he can recount it, answer questions about it, and evaluate it intelligently. Whether a person understands music is shown by how he plays it, how he talks about it, or what aspects of it he appreciates. If someone were to insist that with him understanding is a mental process, we should draw his attention to the differences between the criteria for mental processes and the criteria for understanding (PI p. 181/155). When we are interested in whether he understands something, we are not interested in what is going on ‘inside him’ as it were, what he is doing or undergoing, but in what he can do. Understanding something (an utterance or an algebraic series) is not interruptable as is a mental recitation of a poem. The closest one can get to ‘an interruption’ of understanding is a loss of understanding, or failure of understanding, not a hiatus in a process resulting from withdrawal of attention (Z §85). Suddenly understanding the rule of a series is not something that goes on, lasts as long as, or longer than, the noise of the passing trafﬁc. Understanding the multiplication tables is not a process with a beginning, middle and end, but a gradually acquired ability to operate a calculus. Understanding what someone says is not an articulated process like the utterance of the sentence, nor yet an unarticulated process, for it is not a process at all. One temptation to conceive of understanding as a process is engendered by the similarity between the beginning of a process and the dawning of understanding. On certain occasions, as we have, seen, there are distinctive experiences ‘as the penny drops’. But the dawning of understanding is not the commencement of a process. It is also true that the understanding that consists in the mastery of a complex technique, such as understanding a calculus, is the gradual acquisition of an ability, and that gradual acquisition is processlike. Nevertheless, that process is not the understanding that is its successful upshot. Another temptation to conceive of understanding as a process turned on the thought that understanding the speech of another involves interpreting it — all understanding (of others) is thought to be interpretation. But that is misconceived. Interpretation presupposes understanding and cannot explain it.

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One cannot interpret a sequence of signs that is opaque to one (e.g. ‘abo gol tiftu ineas’), but only ask for it to be translated or deciphered. Then, when it is before one, one can interpret it — if it needs interpreting. Interpreting an utterance is, or is expressed by, clarifying it by means of a perspicuous paraphrase. The need for interpretation typically arises where a sentence can be understood, in its context, in more ways than one, and a good interpretation offers the better way of understanding what is meant. Interpreting, like translating, is indeed an activity or process, but understanding is not. One can begin interpreting a passage, but one cannot begin understanding it (although one might begin to understand it). One can be half-way through interpreting an utterance, but one cannot be half-way through understanding it (although one may ‘half-understand’ it or understand half of it). One can break off interpreting an utterance in the middle, and later resume interpreting, but one cannot break off understanding an utterance and later resume. (c) Understanding is not a mental state Is understanding, then, a mental state? It seems that Wittgenstein, at one stage, thought so. In 1931 he wrote, ‘Being able to and understanding are apparently described as states, like toothache, and that is the false analogy under which I am labouring’ (MS 110 (Vol. VI), 236). He struggled to free himself of this misconception.19 Certainly the verb ‘to understand’ is non-progressive. It is commonly said to lack an imperative form. But that is wrong. It has an imperative form, as is patent in such sentences as ‘Understand this: as long as I am in charge, there will be no squabbling!’ What is true is that one cannot order a person to understand something in the sense in which one can order him to try to understand or to learn, i.e. to do something. But this, though important, is no longer a purely syntactical criterion. ‘To understand’ cannot form a pseudo-cleft sentence with a Do pro-form, its present tense is non-frequentative, and ‘I have understood’ implies ‘I understand’. True, to say that someone slowly understood what was being explained to him is not to say that he did something slowly, but rather that he slowly came to understand. But that again shows that the criteria that determine whether something is or is not a mental state are not purely syntactical. For, syntactically speaking, it is perfectly in order to say of someone that he understood the plans very quickly, or slowly and laboriously. It is an error to suppose that our concept of a mental state is simply the correlate of static verbs, and that it is deﬁned by purely syntactical criteria. 19

It is sometimes thought that PI p. 59/50n.(a): ‘ “Understanding a word”: a state. But a mental state?’ shows that Wittgenstein held that understanding, though not a mental state, is nevertheless a state. However, that apparent concession is misleading, since the source suggests that what Wittgenstein had in mind was that if understanding is said to be a state, then it has to be a state of the brain or of a mind-model (see 4(d) below), against which he argues in PI §149 (see Exg. of both passages).

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Among psychological static verbs by common consensus are ‘mean’, ‘mind’, ‘know’, ‘remember’, ‘forget’, ‘intend’. Although one might classify these as verbs of cognition, they do not pick out cognitive states. One may be in a state of agitation, but not in a state of knowing, remembering or forgetting. Although they are non-progressives, at least some do have imperative forms (e.g. ‘Know thyself !’, ‘Remember me!’, ‘Forget that it ever happened!’, ‘Mind your step!’). Finally, the non-psychological static verbs constitute a very odd bunch: for example, ‘exist’, ‘be’, ‘have’, ‘consist of ’, ‘contain’, ‘include’, ‘belong to’, ‘own’, ‘possess’, ‘involve’, ‘depend on’, ‘cost’, ‘deserve’, ‘ﬁt’, ‘be blue’, ‘be taller than’. One cannot embed any of these verbs in the contexts ‘X was in the state of V-ing’, ‘X was in a . . . state’, or think, for example, of owning, possessing, belonging or having as states of anything. We have a roughand-ready category of states of things and stuffs. We have an equally vaguely circumscribed concept of mental states. Neither are determined by purely syntactical considerations. With respect to types of matter or stuff we have some uncontroversial applications of ‘state’. Being solid, liquid or gaseous are three states of matter. Being molten is a state of aluminium, being frozen a state of water. But while it is true that bronze consists of copper and tin and that high-octane petrol contains lead (both of which are static verbs), consisting of copper and tin or containing lead are not, respectively, states of bronze or petrol. Equally, we speak of the state of a house (e.g. ‘in a dilapidated state’), of a garden (‘well kept’) or of a room (‘untidy’). But owning a house, possessing a garden, a room’s belonging to a person, are neither states of the house, garden or room, nor of its owner (his legal status is not to be confused with his state). Mental states are not a subspecies of the category of state, the other species of which are physical states or states of physical things. Knowing, meaning, intending, forgetting, remembering, etc. are not mental states. We speak of being in a state of intense excitement, deep depression, joyful anticipation, fearful trepidation, irrepressible cheerfulness, etc., but not of being in a state of knowing, meaning something or intending. We may say that we found someone in a state of great excitement, of anxiety or of intense concentration, but not that we found someone in a state of knowing something, let alone in a state of intending or meaning something. Is this merely a triviality, to be overridden by the weightier considerations of developing a philosophical or psychological typology? I think not, for important distinctions are drawn by this classiﬁcation — as Wittgenstein noted — and the exclusion of understanding (like knowing) from the category of mental states in the ordinary sense of this term is no coincidence. Mental states, Wittgenstein stressed, have what he called ‘genuine duration’ (Z §§76–86; cf. Z §488). One can typically ascertain, as it were by spot check, whether they still persist (Z §72; RPP II, §§51–7). Where there is genuine duration, the enduring phenomenon can typically be observed, continuously

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or intermittently (Z §76), but there is no such thing as an uninterrupted observation of my ability to multiply (Z §77) or my understanding of arithmetic. One can determine, for example, the duration of an impression on a stop-watch, but not the ‘duration’ of knowledge, ability or understanding (Z §82). Genuine states of mind typically run a course, ﬂaring up, abating and vanishing (hence one must distinguish emotional dispositions, which lack genuine duration, from emotional states (Z §§488, 491). They have degrees of intensity. If one is in a state of extreme agitation from three to four o’clock, then at any intervening time one is agitated. If one is anxious from ﬁve until six o’clock, then one is anxious continuously. One can interrupt, break into or disturb a psychological state, which may subsequently be resumed, as when one breaks off one’s intense concentration to deal with a triﬂe, and then resumes one’s work, or as when one calms a friend’s acute anxiety only to ﬁnd that he lapses into the same state later. Loss of consciousness is incompatible with the continuity of a psychological state, hence it is ‘Sleep that knits up the ravell’d sleeve of care, / The death of each day’s life, sore labour’s bath, / Balm of hurt minds . . .’. Understanding, like knowing, is not a mental state. There is no such thing as being in a state of understanding. One may understand something from a certain time (the time at which one learnt or understood it) for a certain time (as long as one passes ‘tests’ of understanding, satisﬁes criteria of understanding), i.e. until one forgets or ceases to be able to do such-and-such. But one does not understand it continuously from the time one came to understand it until one ceases (PI p. 59/50n.), as one is in a state of acute anxiety continuously from the time one hears that one’s child is missing until, some hours later, one hears that all is well. One’s intense concentration may be interrupted, but not one’s understanding. One may suddenly lose one’s understanding (one’s grasp) of a problem, and then equally suddenly regain it. But this is not akin to the sudden abating of an acute pain and its subsequent resumption when the analgesic wears off. It is rather like suddenly forgetting and then subsequently recollecting (PI p. 59/50n.; Z §85). One may cease to understand a theorem, a person, a language, etc., but that is not the termination of a particular psychological state. Nor is one’s understanding interrupted or terminated by falling asleep. (d) Understanding is neither a dispositional state of the brain nor a disposition Granted that understanding is not a state of the mind, Wittgenstein raises the question of whether it might not be a state of an apparatus of the mind, either of a ‘mind-model’ or of the brain. Such a state, he suggests, is called ‘a disposition’ (PI §149). That is inaccurate. The hypothesized state is not itself a disposition, since states of things are not dispositions of things. States

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are actualities, whereas dispositions belong to the category of potentialities. But one might call such states ‘dispositional states’ in so far as they are the grounds for the dispositions of their subjects to behave in certain ways. So is understanding a dispositional state of the brain, as has been suggested by Central State Materialism? Witttgenstein makes only one move against this suggestion (PI §149). If understanding were a dispositional state, there ought to be two distinct and independent criteria for understanding. One would be the performances that exhibit understanding. The other would be the obtaining of the hypothesized neural structure, irrespective of performances. If we detected that state N obtained (by means of functional magnetic resonance imaging or positron emission tomography), we should have to say that the person understood, irrespective of what he does. But that is precisely what we would not do. If neural state N were to obtain, but the subject failed to exhibit understanding in a succession of tests, we should deny that he understands. Indeed, we can only discover whatever neural states characteristically accompany understanding one thing or another if we can identify whether the subject understands quite independently of any neural state, and then correlate what neural states we discover with the subject’s possession of the relevant abilities. One might further note that even if we were to discover that certain neural states are well correlated with understanding something, it would be misleading to conceive of them as dispositional states, unless understanding itself were a disposition. If understanding X were a disposition to V, then the inductively correlated neural state might well be characterized as a dispositional state, i.e. a neural state the obtaining of which causes the subject to have a disposition to V. But the moot question that must ﬁrst be resolved is whether understanding is a disposition at all. It is interesting that in the early 1930s, Wittgenstein was inclined to characterize understanding thus. In dictations to Waismann he asserted, more than once, that it is: understanding a word, he said, ‘is a disposition to use this word’ (VoW 359); ‘Understanding a sign can be conceived as a disposition, namely the disposition to apply the sign’ (VoW 369, cf. 441). He stressed that this disposition is essentially something hypothetical, that it is a possibility, not an actuality (ibid.), but also, confusingly, that it is a state (ibid.). To say that understanding is a disposition, he claimed, is like saying that a calculator has a disposition to carry out multiplications. What we are describing ‘is evidently the actual state of the machine’ (ibid.). But this is wrong, as he evidently came to realize. The disposition of a machine to react thus-and-so to a given input is not a state of the machine, for powers of a machine are not reducible to the structures that confer them. Different machines (e.g. calculators) may have the same dispositions or powers, but quite different structures, and in talking of the powers, one is not talking of the structures. It is correct that dispositions of machines and of inanimate objects and stuffs are hypothetical in the sense that to ascribe a disposition to such a thing is to

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say that if such-and-such conditions are fulﬁlled, then the possessor of the disposition will do so-and-so. But, ﬁrst, human dispositions are not simply a species of the genus disposition of which inanimate dispositions are another species. And secondly, understanding is not a disposition at all. Human dispositions are primarily dispositions of health, which do resemble inanimate dispositions, and traits of personality and character, such as dourness, cheerfulness, taciturnity, melancholy, vivacity, sensitivity, delicacy, excitability, placidity and irritability, which do not. (Inanimate objects or stuffs may have a disposition to V in circumstances C, but if C never occurs, the subject of the disposition may never V. By contrast, a person cannot have a disposition of temper or character and never display it.) But understanding is not a disposition, in this sense, at all — it is not a trait of character or part of the nature of a person. Nor is understanding a tendency, proneness, susceptibility or liability. Dispositions and tendencies are essentially characterized by what they are dispositions or tendencies to do. Understanding, by contrast, is characterized by what is understood (in this respect, it is unlike many non-cognitive abilities). To explain that someone V’d because he understood such-and-such is not to explain his behaviour by reference to his habits, pronenesses or tendencies, let alone by reference to his traits of personality. To understand what a given word means is not to be disposed or to have a tendency to act in any particular way or set of ways. If one understands or knows the meaning of ‘antidisestablishmentarianism’ or of an obscenity, it does not follow that one tends or is prone to use this word; nor does it follow that one is disposed, liable or susceptible to respond in any stock way to its use by others, as, if one has a disposition to catch cold, then one tends, if exposed to drafts, to catch a cold. To attribute a ‘psychological’ disposition to a person is to ascribe a trait to him, to characterize his nature, temperament or character. To say that he knows or understands what ‘impecunious’ means is not to do any of these things. For understanding is more akin to an ability than to a disposition or tendency (a point to which we shall return below), and for a person to be able to do something is not for him to have a tendency, proneness or liability to do it.

5. Powers and abilities The concepts of potentiality, power and ability were central to Aristotelian and medieval scholastic philosophy. After the Cartesian revolution in philosophy, despite some honourable exceptions, they were increasingly neglected. In the 1960s and 1970s, a revival of philosophical interest in powers and abilities occurred, stimulated by Wittgenstein and Ryle.20 20

See in particular M. Ayers, The Refutation of Determinism (Methuen, London, 1968); A. J. P. Kenny, Will, Freedom and Power (Blackwell, Oxford, 1976); A. White, Modal Notions (Blackwell, Oxford, 1976).

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A power must be distinguished both from its exercise and from its vehicle, a fortiori from the structure of its vehicle. That an ability is categorially distinct from its exercise should be obvious: the electric kettle one buys (cold and empty) can heat water (otherwise one should not buy it); the car in one’s garage can do 70 m.p.h. (otherwise one should take it to be repaired); a person can speak even though he is silent, can do arithmetic even though he is not calculating, can swim even though he is sitting at his desk. The distinction between an ability and its vehicle is no less important.21 A book can ﬁt into a drawer (and indeed one can see, not its ability, but that it has it). The vehicle of its ability to do so is its shape, but its shape is distinct from its ability. One can measure its shape, but not its ability to ﬁt. Whisky can intoxicate. The vehicle of its ability is the alcohol it contains, but the alcohol is not identical with the intoxicating power. One can weigh the alcohol, but not the ability to intoxicate.22 If an ability is distinct from its vehicle, a fortiori it is distinct from the structure of its vehicle. A pianola can play certain tunes. The vehicle of its ability is the mechanism of drums, pins and wheels. Their structure, the physical interrelation of parts, explains how the pianola can play, but is not identical with that ability. Science explains powers by discovering underlying structures, but it is a mistake to think that it reduces powers to the structures of their vehicles. Hemlock possesses the power to poison; the vehicle of its power is coniine; the molecular structure of that chemical, i.e. 2n-propylpiperidine, in conjunction with principles of physiology and biochemistry, explains how hemlock poisons. But its power to poison is categorially distinct from its chemical structure. By exploiting later systematizations of philosophical misconceptions about abilities, one can clarify and extend Wittgenstein’s critical remarks. One tempting misconception is transcendentalism, i.e. the fallacious reiﬁcation of powers, according to which they are conceived as occult entities mysteriously contained within the possessor of the power. Wittgenstein discusses this: we are inclined to compare the future movements of a machine to objects already lying in a drawer which we then take out, so we think that the possible movements of the machine are already in it in some mysterious way (PI §194). The possible movements are not, of course, the actual movements (they may never occur), nor the physical conditions for moving either (for we say, of these conditions — ‘Experience will show whether this gives the pin this possibility of 21

The distinction is Kenny’s, in Will, Freedom and Power, p. 10. Of course, alcohol itself has the power to intoxicate, and here one cannot distinguish between the possessor of the power and the vehicle of the power. Similarly, the vehicle of the human ability to reason might (but need not) be argued to be the brain or some parts of the cortex, but there is no clear vehicle of the ability to rear children. It is no more surprising that not every human ability has a vehicle than it is surprising that not every human ability has an organ. The organs of sight are the eyes, but there is no organ of thought and reasoning. That a distinction cannot be applied everywhere does not mean that it cannot be applied anywhere.

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movement’, but not ‘Experience will show whether this is the possibility of movement’). So we conceive of the possibility of movement as a kind of shadow of the movement itself. But powers are not invisible sensible properties — they are categorially distinct from actualities, and the categorial distinction is not captured by supposing potentialities to differ from actualities in virtue of being invisible or occult (even though it is true that one cannot see the horsepower of a car under its bonnet). We establish the existence of powers and abilities in diverse ways, some of which may reinforce our proneness to fallacy. We establish that the car can do 100 m.p.h. by driving it fast. The transcendentalist may think that our inference from its performance to ‘a power capable of producing it’23 is one from effect to cause, a thought reinforcing the conception of power as an occult entity. But the inference from ‘AV’s’ to ‘A has the power to V ’ is not such an inference. In reaction to the sins of transcendentalism, two forms of reductionism evolved. The ﬁrst is the reduction of ability to its exercise. The most famous proponent of this form of reduction was Hume: ‘The distinction which we often make betwixt power, and the exercise of it is . . . without foundation’, and ‘is entirely frivolous’.24 Wittgenstein does not discuss this form of reductionism at any length. Rather, having surveyed the variety of grounds for attribution of abilities by means of a large number of imaginary language-games which differently articulate the use of ‘can’ and ‘is able to’ (BB 100–25), he envisages a language-game in which doing a thing is the only justiﬁcation for saying that one can do it. Of this he simply remarks that there is no metaphysical difference between such a linguistic practice and others in which a wide variety of justiﬁcations for attribution of ability are accepted. To adopt Humean reductionism looks like accepting as a ground for attribution of ability only the strongest possible evidence, which is then held to be identical with the ability. Note that there are two moves here: ﬁrst, a grading of evidential support (i.e. the suggestion that V-ing is the best possible evidence for being able to V ), and, secondly, a reduction of ability to performance. Both are mistaken. First, the fact that a person V’s may no more incontrovertibly establish that he has the ability to V than any other evidence; in some circumstances, his performance may have been a ﬂuke, a matter of beginner’s luck (this being one of the many differences between human abilities and the powers of inanimate things). Secondly, sometimes our justiﬁed attributions of powers do not wait upon actual past, present or future performance at all. A round peg (of a given size) can ﬁt into a round hole (of a given diameter) and cannot ﬁt into a square hole (of a given area). It may be prevented from being inserted in the hole, but not through lack of power, rather by circumstances. Nevertheless, the attribution of power may be fully warranted. 23 24

Hume, Treatise, Bk I, pt. iii, sect. xiv. Ibid.

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Thirdly, once the illusion of privileged status of current performance is thus revealed, it is evident that the other kinds of evidence we take as justiﬁcation for attribution of ability are not in principle weaker than current performance qua evidence. Observation of the vehicle of an ability, for example, is not necessarily evidence inferior to that of current performance. One can see that this round peg can ﬁt into that round hole. As regards reductionism, Aristotle’s arguments already sufﬁce to give Hume his quietus.25 If a person cannot do something when he is not doing it, then it is senseless to speak of chess-players, linguists, translators, riders, runners or swimmers. So all attributions of skill are ruled out. With skill disappear the notions of learning and forgetting how to do something. For if an activity must be learnt, yet one cannot do it when one is not doing it, then as soon as one stops, one forgets. Perceptual powers (the ability to see, hear or taste) will be lost when not exercised, so one will be said to go blind when not seeing and deaf when not hearing. So reduction of ability to its exercise is incoherent. A different kind of reductionism is the reduction of an ability to its vehicle or the structure of its vehicle. It is not surprising to ﬁnd this thesis prominent in Descartes, for, as the father of the philosophy of the new sciences, he saw that one form of scientiﬁc explanation is by reference to structures. He mistakenly thought that the geometrical properties (the spatial structure) of material objects and their parts not only explained but constituted their powers (and that all their remaining properties were only effects of this structure upon percipients). Wittgenstein’s discussion of transcendentalism applies equally to vehicle-reductionism. The possibility of the machine’s movement is no more identical with the machine itself or its structure than it is with an occult shadow. We construct the machine in order to give it the possibility of such-and-such a movement. We do not construct the possibility of the movement. Vehicle-reductionism, however, is especially relevant to fallacies concerning mental abilities in general and understanding in particular. We have already surveyed the temptation to conceive of understanding as a mental state. Wittgenstein’s discussion points towards an analysis of understanding as an ability. But in a perverse way this may, if care is not taken, reinforce the fallacious conception of understanding as a state. For one of the standard pitfalls in philosophical analysis of ability is to think that an ability is itself a kind of state. There are . . . various reasons which incline us to look at the fact of something being possible, someone being able to do something, etc., as the fact that he or it is in a particular state. Roughly speaking, this comes to saying that ‘A is in the state of being able to do something’ is the form of representation we are most strongly tempted to adopt; or, as one could also put it, we are strongly inclined to use the metaphor of 25

Aristotle, Metaphysics 1046b29–1047a29.

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something being in a peculiar state for saying that something can behave in a particular way. And this way of representation, or this metaphor, is embodied in the expression ‘He is capable of . . .’, ‘He is able to multiply large numbers in his head’, ‘He can play chess’: in these sentences the verb is used in the present tense, suggesting that the phrases are descriptions of states which exist at the moment when we speak. The same tendency shows itself in our calling the ability to solve a mathematical problem, the ability to enjoy a piece of music, etc., certain states of mind; we don’t mean by this expression ‘conscious mental phenomena’. Rather, a state of mind in this sense is the state of a hypothetical mechanism, a mind-model meant to explain the conscious mental phenomena . . . In this way also we can hardly help conceiving of memory as a kind of storehouse. Note also how sure people are that to the ability to add or to multiply or to say a poem by heart, etc., there must correspond a peculiar state of the person’s brain, although on the other hand they know next to nothing about such psychophysiological correspondences. We regard these phenomena as manifestations of this mechanism, and their possibility is the particular construction of the mechanism itself. (BB 117f.)

Abilities, powers and dispositions, though they may be acquired, possessed for a time, and perhaps later lost, are not states. A new car can do 120 m.p.h. (even though its owner is not so rash as to drive it at that speed), but its being able to do 120 m.p.h. is not a state of the car. An old car, by being overhauled, may be brought into a state in which it can, again, do 120 m.p.h., but its ability is not the state of its pistons and carburettor. Rubber, in its solid state, is elastic, but its being elastic (unlike its being compressed) is not a state of the lump of rubber. Burning rubber is in a state of combustion, yet being combustible is not a state of rubber but a passive power or disposition of rubber. Sugar is soluble, but solubility is not a state of sugar. So too with characteristic human psychological abilities and dispositions. Being able to speak French, play chess or conjugate Latin irregular verbs are not states of a person. Being clever, intelligent, charming or dull are not kinds of mental states, nor are understanding, knowing or remembering. One may interrupt a person’s exercise of his intelligence, manifestation of his understanding, and display of his knowledge, but not his intelligence, his understanding or his knowing. One may, through senility, cease to be intelligent, no longer understand some complex mathematical theorem, and no longer know much that one once knew. But loss of intelligence, understanding or knowledge is not termination of a state. Dispositions (such as traits of character) and abilities, though possessed for a time, do not have genuine duration. One may continue to possess them, but they are not continuous anythings. They belong on the same shelf as potentialities, not on the shelf of actualities. Although behaviour manifesting understanding is not itself understanding, but evidence for it, what this is evidence for is an ability, not a state. Central State Materialism errs much as Wittgenstein anticipated: to speak of an object’s having a dispositional property entails that the object is in some non-dispositional state or that it has some property (there exists a ‘categorical basis’)

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which is responsible for the object manifesting certain behaviour in certain circumstances . . . if brittleness can be identiﬁed with an actual state of the glass, then we can think of it as a cause, or, more vaguely, a causal factor, in the process that brings about the breaking. Dispositions are seen to be states that actually stand behind their manifestations. It is simply that the states are identiﬁed in terms of their manifestations in suitable conditions, rather than in terms of their intrinsic nature. Our argument for a ‘Realist’ account of dispositions can equally be applied to capacities and powers. They, too, must be conceived of as states of the object that has the capacity or power.26

There is a puzzle about this confusion. We are not tempted to identify the horsepower of our car with a state of its engine. We do not identify the possibility of a machine’s movements with the structure of the machine that makes them possible. So why is vehicle-reductionism so tempting in the case of mental powers, and in the case of reduction to molecular structures — as in the case of brittleness or solubility? The reason, perhaps, is a miscegenous crossing of transcendentalism and reductionism. There is a sense in which we cannot observe powers (there is no such thing in such cases as observing the power), but only their manifestations. Yet, we contend, the manifestation occurs because the object has the relevant power. The transcendentalist conceives of the power as an invisible entity within the object (a kind of soul) which causes the manifestation. Science explains how objects can do what they can do by discovering underlying structures. Where the structure is visible (as in the case of the internal combustion engine), we are not greatly inclined to identify the power with the structure. But where the structure is not visible, as in the case of the molecular structure of brittle objects, the transcendentalist picture more readily intervenes, inclining us to identify the disposition (passive power) with the (no longer occult but still unobservable) structure which explains it, and hence to conceive of the disposition as the cause of its manifestation. A fortiori, in the case of human abilities such as understanding, we note that the manifestation of understanding is distinct from understanding. We are already inclined to think of understanding as a state, and consequently we jump to the wholly erroneous conclusion that it is a state of the brain which is the hypothetical cause of manifestations of an ability. But an ability is not a state, nor is it the cause of its manifestations; it is not a visible entity with an observable structure, but neither is it an invisible entity with an unobservable structure.

6. Understanding and ability If we wish to ﬁnd the shelf upon which to locate understanding, then it is together with abilities. ‘The grammar of the word “knows” is evidently closely related to that of “can”, “is able to”. But also to that of “understands” ’ 26

Armstrong, A Materialist Theory of the Mind, pp. 86, 88.

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(PI §150). In a dictation to Waismann, Wittgenstein said that ‘understanding the meaning of a word is comparable with what we call an ability or capacity. That is, there is a kinship between the grammar of “can”, “is able to”, and that of “understands the meaning”. One could indeed even state that understanding the meaning is the ability to apply the word correctly’ (VoW 357, modiﬁed translation; cf. AWL 92).27 One can ask someone since when he has been in a certain mental state, for example in pain, in a state of intense concentration or feeling cheerful — and the reply may be, ‘Since lunchtime, continuously’. One can ask someone since when he has understood a certain word. But one cannot ask whether he has understood it continuously, and he cannot answer, ‘Since lunchtime when it was explained — without a break’ (PI p. 59/50n. (a)). One can ask ‘When do you get depressed?’ — and the answer may be ‘Whenever I hear such-andsuch bad news’. But ‘When do you understand the meaning of “W”?’ is as anomalous as ‘When do you have the ability (when do you know how to) to play chess?’ (PI p. 59/50n. (b)).28 Understanding (knowing) what a word means, unlike experiences, mental states and processes, and like abilities, lacks genuine duration. One no more ceases to understand what one understands when one falls asleep than one ceases to know what one knows. The criteria for understanding are akin to criteria for potentialities (tendencies, pronenesses, dispositions, habits, abilities, liabilities), not to criteria for actualities. A person who understands something is able to do certain things. It might be objected that we need to distinguish between a dispositional sense of ‘to understand’ and an occurrent sense.29 The dispositional sense is involved in understanding a word, phrase or sentence considered as a type. In this sense, one understands (or knows the meanings of ) words, phrases and sentences of English, if one has learnt English. This is indeed an ability: namely, an ability to frame sentences expressing thoughts, and an ability to understand (in an occurrent sense of the word) the thought or proposition expressed by sentences in use. But, the objection continues, Wittgenstein was mistaken to think that there is no occurrent sense of ‘to understand’. Indeed, Frege had pointed out that we need such an occurrent sense in order to describe what 27

Interestingly, parallel to BB 117 quoted above, he goes on immediately to warn that this explanation still does not get us out of the woods, since the same confusions are engendered by the word ‘ability’ as by the word ‘understand’. For we are tempted to construe an ability, no less than understanding, as a state. So we think that the ability to use a word correctly is, as it were, the hypothetical reservoir from which the applications of the word ﬂow. Wittgenstein warns again and again that it is a pervasive and pernicious error to suppose that in some sense ‘in the understanding of a word all of its future applications are pre-existent or dormant’ (VoW 369). 28 It is no coincidence that the normal use of ‘When can you play chess?’ is a question about opportunity, not ability. 29 The objection is derived from M. A. E. Dummett, The Origins of Analytic Philosophy (Duckworth, London, 1993), pp. 58–60, 101–3, 109, 133. This is well criticized in B. Rundle, ‘Meaning and Understanding’, in Wittgenstein: A Critical Reader, ed. H.-J. Glock (Blackwell, Oxford, 2001), pp. 109f.

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happens when the thought expressed by an utterance is grasped (PW 145). Otherwise understanding an utterance would amount to no more than hearing it, while possessing a dispositional understanding of the constituent words and sentential structure. But that cannot be right, since we are often perplexed by an utterance at ﬁrst, and only understand it after reﬂection. Moreover, we need the distinction to budget for indexicality and ambiguity. For we distinguish understanding a type-sentence containing indexicals or an ambiguous word or structure from understanding what a token of it is used to say on an occasion. This confuses different objects of understanding with different senses of ‘understanding’. There is indeed such a thing as understanding words, phrases and sentences understood as types, and that is distinct from understanding an utterance on an occasion. But this does not involve two different senses of ‘to understand’, but two different kinds of objects of understanding. Moreover, the objection misconstrues Wittgenstein’s claim. To assert that understanding is (akin to) an ability is not to assert that there is such a thing as ‘a dispositional understanding’. It is rather the claim that understanding is a cluster of abilities (not dispositions) — to understand is to be able to do various things. To distinguish between understanding in a dispositional sense and in an occurrent sense would commit us to the view that understanding in the former sense is a disposition to understand in the latter sense if an occasion should arise. But that is confused. To understand a word, phrase or sentence considered as a type is, inter alia, to be able to explain what the expression means and to be able to use the expression in a speech-act. To understand a particular utterance on an occasion is, inter alia, to be able to explain what was said and to be able to respond appropriately. But surely, one might remonstrate, when one understands an utterance, something happens (one grasps a thought, as Frege insisted). To be sure, when one understands an utterance, one understands what was said by the use of the sentence in question. Is that more than ‘possessing a dispositional understanding and hearing the utterance’? It is, of course, more than understanding the constituent words of the utterance and being familiar with the sentential structure. It is being able to explain what was said and being able to respond to it appropriately — and that is not an occurrence. Understanding thus may be immediate and unreﬂective, or it may require reﬂection. But what is occurrent, and what is signalled by the utterance ‘Now I understand!’, is the dawning of an ability, not the performance of a mental act signiﬁed by the verb ‘to understand’ in an occurrent sense. In such an utterance, the verb ‘to understand’ is used in a manner akin to achievement-verbs such as ‘win’ or ‘ﬁnd’ to signal something that does not take time but occurs at a time. Like beginning to move or ceasing to move, suddenly understanding something marks a change — from incomprehension to comprehension, hence from not being able to do those things that one who understands that thing can do to being able to do them.

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Nevertheless, categorizing understanding as an ability simpliciter would be misleading. It is more correct to say that understanding is akin to an ability, or that in its dominant uses ‘understanding’ signiﬁes an ability. Why did Wittgenstein adopt this cautious formulation? The ﬁrst point to stress is the diffuseness of understanding in comparison with the generality of abilities. This is visible in the following two features. (i) If understanding is an ability, it is not an ability to do, for every item one understands, one single type of thing or uniform class of things. This distinguishes understanding from many, though by no means all, kinds of abilities. A person who understands a sentence of his native tongue can do many things: for example, paraphrase it, explain it, use it in appropriate contexts, respond to it in appropriate ways. A person who understands children can get on well with them, make himself loved by them, communicate his sympathy to them, play with them to their delight, grasp (understand) their motives and their complex symbolic behaviour (in particular their displacement behaviour), and so on. This large variety of abilities of which different understandings may consist does not merely reﬂect the multiple criteria for understanding. (Pain too has multiple criteria, but lacks the inherent complexity of the concept of understanding.) (ii) Understanding, over a wide range of its objects, is more passive than some of the abilities which are associated with such objects. Understanding German is not the same as being able to speak German, since one may understand yet be unable to speak (although one can say what a German sentence means). Understanding music is not the same as being able to play or compose; nor is understanding art being able to paint or sculpt. Secondly, there are degrees of understanding which are not reﬂected in the degrees to which a given ability is possessed. Abilities are often capable of degrees: the more able one is to do such-and-such, the more excellent one’s performances are likely to be. But degrees of understanding do not always result in a more skilful execution of some act or activity. We may speak of a deepening of our understanding of a late Beethoven string quartet, although there may be little if anything that we can do as a result. Criteria for the change may lie in the way we listen and the delight we take in the music. It is very often our attitudes that change with the deepening of our understanding, not our abilities. The deepening of our understanding for a person may amount to no more than a more generous empathy or effort of imagination. And lest it be thought that this depth is uncharacteristic of understanding language, reﬂect on the deepening of understanding of a poem with maturity. Thirdly, if a person understands an explanation of the meaning of ‘W’, then he understands the word, knows what it means. This internal relation between explanation, meaning and understanding is a general feature of linguistic understanding. But it is not, in general, a feature of practical abilities. There is, all too frequently, a wide gap between understanding the explanation of how to V (e.g. ride a bicycle) and being able to V. Where V-ing is such an

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activity, it is not a criterion for not having understood the explanation of how to V that one should fail to V. But a criterion for my not understanding a grammatical explanation of ‘W’ is that I go on to use ‘W’ incorrectly. There are, as we have already seen, different objects of linguistic understanding. Reﬂect on the differences between understanding a nonsense poem, understanding an English sentence out of context, understanding the same sentence in context, understanding what is said by its use in context, understanding what is meant by it, and understanding what is meant by uttering it. Similarly, reﬂect on different types of lack of understanding manifest in the following sentences (cf. PLP 347): I I I I I

cannot cannot cannot cannot cannot

understand understand understand understand understand

you, you, you, you, you,

you must speak louder. that is sheer nonsense. I don’t speak German. what you said was too complicated to follow. I don’t see why you want . . .

To which one may add: I I I I

understand what he said, but I can’t understand the joke. understand what he said, but I don’t understand why he said it. understand the words all right, but I don’t understand to whom they refer. understand what he said, but I can’t understand whether it was a threat or a promise.

Waismann concluded from such cases that ‘to understand’ is ambiguous, sometimes signifying an experience, sometimes a process or a state, in other contexts an ability, and so forth. In the early 1930s Wittgenstein’s position was indeed equivocal. He spoke of the ambiguity of the word ‘understand’ (PG 49), but also of its being a family-resemblance term (PG 74f.), signifying a family of processes. Yet he remarked that calling understanding ‘a process’ produces a false grammatical attitude towards it (PG 85). He suggested that understanding is sometimes a process and sometimes a state (PG 82), but also that the word may mean an ability (PG 47). This unsatisfactory position is mirrored in Waismann’s contention that in one of its uses ‘understand’ stands for a mental reaction, but in others understanding is not an experience but a disposition, or merely a piece of behaviour appropriate to a sentence (PLP 347f ). The Principles argues that the word ‘understanding’ was gradually extended from a core of characteristic cases to others more or less akin to it. Understanding consists of ‘a whole bundle of processes, dispositions, experiences, patterns of behaviour which are bound together by language into a sort of unity’ (PLP 348). But in the next sentence Waismann proceeds to speak of ‘this ambiguity of “understand” ’. The Investigations irons out most of these wrinkles. Understanding, Wittgenstein now argues, is not an experience (PI §153), a mental process (PI §§152, 154), or a mental state (PI p. 59/50n. (a), §149), although it has

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afﬁnities with each of these. But it has a closer kinship with being able to do something. He now rejects the suggestion that ‘understand’ is polysemic, but does not explicitly commit himself to the view that it is a family-resemblance term: ‘I would rather say that these kinds of uses of “understanding” make up its meaning, make up my concept of understanding. For I want to apply the word “understanding” to all this’ (PI §532). Is understanding, then, an ability? Perhaps one can best encapsulate the truth in a metaphor (cf. PLP 346): the grammar of ‘understands’ and ‘is able to’ run for a stretch over parallel tracks (cf. PI p. 192/164). The clariﬁcation of the categorial status of understanding, in particular of understanding a word, does not by itself resolve the problem posed in §§138– 41: how can what one grasps at a stroke ﬁt the use of the word? The elucidation enables us to exclude various tempting explanations: namely that, in one way or another, the subsequent applications of the word are already laid up in the understanding. But the question still needs to be resolved: how is the meaning of a word, which is given by an explanation of meaning and which is grasped at a stroke when someone understands what a word means, related to its applications over time? What is the relationship between a rule (such as an explanation of meaning) and its applications (its correct use from occasion to occasion)? If someone understands an explanation of meaning, grasps the rule for the use of a word, he is able to follow the rule in his applications of the word. But what is involved in following a rule and in something’s following from a rule? These questions are the theme of §§185–242 of the Investigations.

Wittgenstein: Understanding and Meaning Part I: Essays G. P. Baker, P. M. S. Hacker Copyright © 2005 by G. P. Baker and P. M. S. Hacker

Index

Page numbers in bold indicate an extensive discussion of the topic. a priori order 17, 253f., 262, 264 –9, 271, 274 ability 292, 375–80, 380 –5 vehicle of 376, 378 acquaintance 10, 24f., 109f., 114f., 116, 125 aesthetics, explanation in 321 agreement with reality 343f., 350 agreement, in deﬁnitions 34, 91, 100, 136f., 147n. in judgements 91, 138, 147n. Alexandria, library of 273 ambiguity 8f., 246 Ambrose, A. 57n. analysis 35, 54, 70, 81, 121, 140, 166, 202, 203f., 205, 206, 211, 221, 254, 272, 281, 305, 327 anti-realism 134n. argument see philosophy, argument in Aristotle 5, 12, 141, 164, 166, 201, 206n., 215, 271, 378 arithmetic 46f. Armstrong, D. M. 367, 379f. Arnauld, A. 12n., 133, 165, 201f., 206n. assertion 19, 34, 66, 76 – 80 assertion-sign 71, 77f. assertoric force 22 assumption see Frege, his concept of Augustine 1–3, 5, 12, 13, 55, 60, 129, 189, 191, 251, 283, 302, 332n. Augustine’s picture 1– 3, 5, 11, 28, 65, 81, 168f. Augustinian conception of language/ meaning 1–28, 31, 74, 92, 134f., 142, 164, 171, 337, 341 avowals 59, 122, 345 Ayer, A. J. 287 Ayers, M. 375n.

Bacon, F. 133 Bain, A. 207f., 218 Baker, G. P. 161n., 174n., 176n., 273n. beauty, the beautiful 207n., 210n. behaviourism 186f. belief 278, 280, 330f., 336 Bentham, J. 172f., 279n. Benthamite archetypes 178 Berkeley, G. 164, 291 bipolarity 119, 338, 343 blindness, and mastery of colour concepts 101 blindsight 278 Bolinger, D. 367 Boltzmann, L. 311–14, 317 Brouwer, L. E. J. 354 Caesar, Julius 24, 32, 345 calculus conception of language see language, calculus conception of Carnap, R. 7, 8n., 83, 98n., 134, 135n., 138, 291, 300, 302 categories see grammatical categories Central State Materialism 367, 374, 379 centres of variation 59, 319f. Cephalus 37 certainty 278 chemical analysis 203f. chess 47f., 147, 292, 330f., 348 analogy with language 46 –9, 52f. Chomsky, N. 9n., 11n., 14n., 175, 183, 184, 358, 365f. Churchill, W. S. 245 Ciofﬁ, F. 321n. clarity 308f. cluster concept 217 colour 9, 55, 91f., 96f., 101, 104, 105, 123, 127f.

388

Index

colour exclusion 24, 46 colour octahedron 328 Comenius, J. A. 6 command (order) 19, 66, 68, 79f. common properties 206f., 209, 210, 213, 214, 216, 217, 218 complete/incomplete 37 compositionalism 139, 173 – 81, 230, 231, 246 computationalism 14, 162f., 173, 176, 181–7, 230, 358 conceptual geography see logical geography Condillac, E. B. de 133n., 202 connection between language and reality 6f., 7, 16, 17, 81f., 92, 95f., 106, 135, 144, 145n., 149 context(ual) principle(s) 5, 48, 124, 139, 159–87 contradiction 279 conversational implicature 146n. conversion principles 192, 196, 198 Copernican revolution 269, 271 Copernicus, N. 312 Darwin, C. 312, 315 David, J.-L. 342 Davidson, D. 10n., 67n., 140, 175 deﬁnition, analytic 16, 30, 35f., 221, 225, 282f. deﬁnition, nominal 201–3 deﬁnition, ostensive see ostensive deﬁnition deﬁnition, real 201–3, 205, 211n. deictic gestures 85f. demonstratives 107, 108, 110, 111, 112, 117, 247f., 257f. depth grammar 134, 177, 256, 309 Descartes, R. 6, 121, 164, 202, 204, 271, 276, 366, 378 description 3, 15, 18, 20, 22, 65, 68f. determinacy of sense 123, 204f., 206, 255, 261f., 338 discourse functions 75, 138 dispositions 374f. dogmatism 263, 297f., 322f. Dummett, M. A. E. 67n., 97f., 175, 183, 381n. Einstein, A. 189 elementary propositions 260, 336, 338

45f., 139n., 254,

Ernst, P. 314f. essence 1, 3, 13, 120, 211, 252f., 254, 264, 271, 282, 309 essentialism 201–12 existence attributions 115, 119, 125f. explanation 29 – 43, 218, 219, 234, 283, 296 and application 38, 41, 87f. completeness of 37f., 87, 88 correctness of 41, 87 criteria of success of 33, 36f. diversity of 35f. by examples 213, 217, 219, 220 of meaning 1f., 8, 15, 16, 17n., 29 – 43, 82, 83 – 8, 132, 146f., 152n., 155, 179f. extensionality 339 facts 170, 336 ‘family-likeness’/‘-resemblance’ 209f. family-resemblance concepts 36, 38, 43, 51, 201–26, 252, 268 of formal concepts 224 – 6 of psychological concepts 222– 4 Faraday, M. 312 Feigl, H. 7 Fischer, E. 186n. ﬁtting/belonging 348 focal meaning 215 Fodor, J. 183 following a rule 89, 102, 185f. force operator/indicator 13, 19, 20, 79 form of representation 257f., 263 – 6, 268f. formal concepts 28, 224 – 6 formalism 46f., 324n. Frazer, J. G. 315, 319, 320, 326, 327 Frege, G. 1, 4, 5, 14, 18, 19 –23, 25, 26, 27, 28, 33, 37, 40, 45, 66, 67n., 72, 79, 96, 133, 134, 140, 146, 148, 171, 203 – 5, 206, 207, 218, 222n., 227, 251, 273, 282, 283, 289n., 290, 291, 293, 300, 338, 339, 342, 364 and anti-psychologism 39, 66, 137, 160, 166f. and compositionalism 174 and computationalism 14n., 162f. his concept of an assumption (Annahme) 65, 71, 77, 79

Index his concept of a concept 13n., 21, 36, 40, 203, 204f. his concept of an object 13n., 20, 21 his concept of sense 23, 66, 161f., 174, 230f., 233f., 244f. on contents of judgment/thoughts 70, 77, 78, 161, 166 on context principles 20, 48, 159 – 64, 165 –70 on decompositional analysis 20, 166, 174n. and function-theoretic logic 21f., 166, 231 on indexicals 108f., 111 on meaning (Bedeutung) 20, 21, 23, 143, 245 his meaning-body conception 13n., 20 on number 32, 47, 152n., 168, 169, 211f., 281, 345f. on primacy of judgement 20, 165f., 167, 169, 174 on proper names 230f., 244f. on thinking 161 on thought building-blocks 174f. on understanding 174n., 183, 358, 381f. Freud, S. 279, 286, 315, 320, 327 Galilei, G. 273 Galtonian method 57n. game, analogies and disanalogies with language 49 – 54 concept of 51, 216f., 220 deﬁnition of 215n. family-resemblance character of 51, 209, 212 –17 general propositional form 3, 51, 208f., 260f., 264, 272f., 280, 335, 339 – 44, 346, 348 genuine duration 372f., 381 gesture-language 92 given, the 17n. Goethe, J. W. von 122, 239n., 259, 313, 315 –20, 322, 325, 326, 332 Goffman, E. 215n. ‘good’ 31, 210n. grammar 35, 145f., 147f., 289f., 291, 300f., 324, 325, 327, 328, 327– 34 analogy with rules of games 52

389

autonomy of 16, 147, 191 depth see depth grammar misleading features of 277, 280 surface see surface grammar tabulating rules of 292, 327, 330, 333 grammatical categories 5, 16, 179 grammatical form 277 grammatical models 56f. grammatical proposition 105, 151, 264f., 265n., 291, 298f., 329n., 331, 332, 341, 353, 354 Greenbaum, S. 364n. Grice, H. P. 134, 146n., 150n. Hacker, P. M. S. 161n., 174n., 176n., 273n., 321n. Hardy, G. H. 329f. Hare, R. M. 67 harmony between language and reality 122f. Heine, H. 46 Helmholtz, H. von 312 Herder, J. G. 133n., 240, 316 Hertz, H. 311, 312, 313 Hobbes, T. 11n., 21, 133, 202, 203n., 360 Hugo, V. 239n. Humboldt, W. von 209 Hume, D. 133, 164, 276, 278, 281, 377, 378 Husserl, E. 273n. hydrodynamics 318f. hypotheses 56n. ‘I’ 54, 108n. iconography 129f. idealism, linguistic 8, 133, 365, 368f. ideas 9n., 39n. private ownership of 137n. simple 204, 258 identity statements 232, 238, 246 images, mental 369 incomplete symbols 113f., 115, 116 indeﬁnables 6, 8n., 10, 16, 24, 35, 114, 120, 128, 144 indexicals 107–12, 247 instruments 75, 76 intentionality 10, 122f., 141f., 255f., 280, 291f. intermediate links 310

390

Index

internal properties 120, 132n., 337 internal relations 96f., 105, 134 interpretation 10, 14, 18, 27, 150, 358, 370f. James, W. 208n., 278, 322, 362, 363, 366 James–Lange theory of emotions 324 Johnson, W. E. 7 Jones, W. 209 Kant, I. 22, 165, 269, 271, 276, 294 Katz, J. J. 183 Kenny, A. J. P. 364n., 376n. Keynes, J. M. 272f. Kirchhoff, R. 312 Kneale, M. 203n. Kneale, W. 203n. ‘know’, use of 345 knowing what a word means 9 –11, 24, 27, 40, 41–3 knowledge, foundations of 121f. knowledge, tacit 185, 325n. Kripke, S. 195n., 238 Künne, W. 349n. language 1–28, 29 – 43, 45 – 64, 65 – 80, 129 –58, 159 – 87, 208 –10, 251, 253 – 6, 259 – 63, 272, 277– 81, 300 –2 calculus conception of 34f., 45, 47–50, 55, 64, 162, 176, 177, 179, 181 deﬁnition of 51, 224f., 262 essence of 1–3, 14, 27f., 51, 254, 259 as a family-resemblance concept 51, 224f., 268f. foundations of 2, 10, 16, 17f., 121f., 259 innate knowledge of 30 instruments of 61 learning 30, 58f., 62, 329 sublimation of concept of 262 teaching 30 –3, 58f., 62, 87 of thought 19, 27 training 30f., 62, 84, 87 language-game 3n., 18, 45 – 64, 293, 329 invented 60, 61f., 330, 332f. natural 63f. primitive 58f., 59 – 61, 292 Leech, G. 364n. Leibniz, G. W. 202

Lichtenberg, G. C. 302 linguistic idealism see idealism, linguistic linguistic turn 272 Linnaeus, C. 316 Locke, J. 4, 5, 6, 7, 9n., 10, 21, 133, 164, 202n., 203, 289 logic 266 –9, 271, 273n., 337f. crystalline purity of 252, 267f. multi-valued 354f. presuppositions of 337 propositions (laws, truths) of 45f., 68, 253, 338f., 354 sublimity of 252, 253 – 6, 309 logical atomism 113 –20, 121, 125 – 8 logical connectives 22, 24f., 28, 85, 351 logical experience 10, 24, 114 logical form 105f. logical geography 284f., 287f., 309f., 329, 333f. logical propositions see logic, propositions of logical truths see logic, propositions of logically proper names see names, logically proper Loos, A. 320 Lukasiewicz, J. 267f., 354f. Lyons, J. 364n. Malcolm, N. 280n., 286n., 287n., 321n. mathematical logic 282 Maxwell, J. C. 312 meaning (Bedeutung) 2, 29f., 33 – 5, 124, 129 – 58, 234f., 357f. desiderata for account of 136 – 44 explanation of see explanation of meaning ﬁgurative 178 of a sentence see sentence, meaning of theory of see theory of meaning for a language transparency requirement 140, 151f. and use 15, 19, 40, 41, 49, 62, 73 – 6, 145 – 58, 186, 290, 291, 292f., 309, 325, 329, 357f. of a word 4 –7, 10f., 15, 16, 19, 22, 23f., 39f., 130, 131, 132, 133, 138f., 140, 141, 143f., 146 – 51, 152, 153, 154, 156, 157f., 159f., 171, 176, 177, 186

Index meaning (meinen) 6n., 9f., 18, 26f., 73, 131, 149f., 256, 261, 268, 292, 331, 359f., 361 meaning-body (Bedeutungskörper) 5, 13, 19, 152 measurement 99f., 189 –92, 196 mental state see state, mental mental process see process, mental metaphor 178f. metaphysical use of words 290f. metaphysical necessity 104, 105, 264f. metaphysics 253, 271, 281, 283, 295f., 304, 337 method of projection see Tractatus on Mill, J. S. 4, 12n., 133n., 202, 207f., 218, 238 modus ponens 77f. mood operator see force operator Moore, G. E. 40, 62, 171, 205, 210n., 281, 283, 348n., 350 Morandi, G. 342 Mörike, E. 243 morphological method 317f., 321f., 326, 332 Morris, C. 134 multi-valued logic see logic, multi-valued myth 314, 315 mythology of symbolism/psychology 283 name 1, 2, 4 –11, 15, 20, 26f., 323f. idealization (sublimation) of 120f., 258, 259, 266 logically proper/simple 6n., 26f., 109 –11, 113 –28, 258 proper see proper names name-relation 6n., 112, 116, 119, 126, 128 naming 1, 15, 163, 172 Napoleon Bonaparte 341f. necessary existents 104, 119, 123 necessary truths 9, 17, 24, 96f., 119 necessity, metaphysical see metaphysical necessity Newton, I. 281, 302 Nietzsche, F. 209, 314n. nonsense 13, 19 number 32, 40, 47, 84n., 152n., 205, 213n., 345f. number-words 40, 83f., 152n., 206f.

391

object see simple object; also Frege’s concept of; Tractatus conception of Ogden, C. K. 134 order see command oriental despot 54 ostensive deﬁnition 7–9, 16, 17, 41, 43, 81–106, 128, 142, 192 completeness of 9, 87f. and description 10, 82, 90, 102 mental 7 normativity of 88 –92 as substitution-rule 90 ostensive explanation 2, 7–9, 10, 17, 82 overview (Übersicht) 32, 42, 281, 284f., 289f., 292f., 307– 34 pain 59, 348n. Palmer, F. R. 364n. Pascal, B. 303 Peter of Spain 164 philosophy 271– 306, 309 argument in 294 depth of 299f. and common sense 302 and discovery 296f. and explanation 296 and grammar 289f. hypotheses in 295f., 310 and linguistics 300f. methods of 275, 288, 290 – 4 and ordinary language 301f. problems of 274, 277– 83, 300, 323, 325 and progress 306 and psychoanalytic analogy 286f. and recollection 295 and science 281f. and skill 275f. and systematicity 302 theory in 294f. as therapy 285f. theses in 15, 294f., 297–9 Tractatus, on philosophy see Tractatus trivialization of 301 picture theory of meaning/of the proposition 66, 170, 211, 224f., 254f., 258f., 280, 336f., 340, 341f., 350 pictures in language 279f.

392

Index

Plato 12, 33, 60, 121, 148, 164, 201, 210, 211, 271, 273, 274, 276, 282, 332n. Platonism 103, 324n. playing 214 pointing see deictic gestures power 375 – 80 practice 34, 62, 89, 137f. primal plant 315 –17, 318f. private language arguments 150 process, mental 369f. proper names 49f., 121, 124 –7, 227– 49 abbreviation theories of 230 –3, 238 allocation of 241f. causal theory of 228, 238 cluster theory of 233 – 5, 238 complex 242f. and deﬁnite descriptions 232 etymology of 241 explanation of 237, 238 meaning of 124f., 143n., 154, 227f., 234f., 244 –9 ostensive explanation of 247 understanding of 235 –7, 248f. uses of 228f., 236, 237, 240 vacuous/empty 229f., 239, 243, 246 proposition 15, 32, 66, 68, 72f., 164f., 171–3, 211, 224, 225, 254f., 258, 324, 335–55 as family-resemblance concept 225, 268, 278, 340f., 345, 354 complexity of 164, 171f., 342f. idealization of 258f., 260, 266 propositional attitudes 72f. propositional functions 170 propositional jingle 344f. propositional system see Satzsystem propositions of logic see logic, propositions of psychoanalysis 286f., 315 question 19, 66, 68 Quine, W. V. O. 8n., 98n., 303n. Quirk, R. 364n. ‘quite particular’ 261 Ramsey, F. P. 12n., 135n., 140 recognitional abilities 91, 97, 100f. reduction 281 Reid, T. 8n., 203n.

Richards, I. A. 134 rigid designators 229 ritual, explanation of 320f. rule 33, 35, 88f., 91f., 146, 185f., 220, 328, 358f. essential/inessential 47n., 155 hidden 217f., 358f. Rundle, B. 142n., 153n., 215n., 381n. Russell, B. 1, 4, 6n., 9n., 14, 18, 23 – 6, 27, 28, 45, 46n., 54, 72, 82, 124, 134, 135n., 136f., 140, 143, 146, 170, 205f., 227, 251, 272f., 282, 289n., 291, 293, 299n., 300, 338, 339, 342, 348n., 354 on indexicals 109f., 117 on logically proper names 109f., 113 –22, 127 on meaning 23f., 136n. on philosophy 304 on proper names 117, 231–3 on propositional content 70, 71n. on sentence-radical 13n. on truth 12n., 25, 350 on universals 24, 115 Ryle, G. 284, 375 sample 7, 8, 17, 36, 41, 43, 82, 91, 92 –103, 128, 191, 194, 195 canonical 36, 99, 102, 192– 4, 196 mental 8, 89 optional 36, 100, 101, 102 standard 36, 99, 102, 191, 193 samples and simples 103 – 6, 123f. Satz 73 Satzsystem (propositional system) 46 Schelling, F. W. J. 175 Schiller, F. 259, 317 Schlegel, F. 209 Schlick, M. 4, 6n., 7, 83n., 256, 308, 327 Schopenhauer, A. 209 science 311–14 methods of 281 models in 312 seeing aspects 310 self 322 semantics 134f. sense data 56, 115, 116, 121f. sense, determinacy of 45 senselessness 338f.

Index sentence 2f., 173 context dependence of 180f. as descriptions 18, 22, 65 – 80 descriptive content of 70 –3, 78f. essence of 11, 13, 15, 20, 25, 67f. form of 75f. function of 18f. as instrument 73 – 6 meaning of 11–14, 73, 130f., 135, 137, 138f., 180 one word- 12, 18, 159, 343 uses of 65–80, 130f., 131f., 136, 173, 180 sentence-radical 13, 19, 20, 22, 67, 70 –3, 79, 139, 177 showing/saying 253, 254, 271, 304, 351 similarities in the large/small 221 simple natures 204 simple/complex 17, 127f. simple object 17, 103 – 6, 258 Socrates 55, 201, 210 Spengler, O. 263f., 317, 320, 326, 332 Spinoza, B. 202 Sraffa, P. 342 standard metre 189 –99 state 372 state, mental 9n., 223, 371–3 Stewart, D. 207, 208, 209 Strawson, P. F. 305n., 354 sublimation of expressions 121, 252, 259, 262 surface grammar 55, 268, 309, 322 surveyability see overview surveyable representations 307, 308, 316, 320, 326–34 Svartvik, J. 364n. symptoms/criteria ﬂuctuation 135 synonymy 156 synthesis, method of 202f., 205 tabulating rules see grammar, tabulating rules of Tarski, A. 67n., 138, 139n. theory 281, 294f., 302 theory of meaning for a language 66f., 175, 182 Theory of Types 25, 116 Theory of Descriptions 116, 120, 305 theses in philosophy see philosophy, theses in

393

thinking 19, 27, 223, 280, 360 and operating with symbols 331 Thomae, J. 46 Thomson, J. J. 312 thought-constituents 11 thought, speed of 325 thought building-blocks see Frege, on thought building-blocks tools 75 Tractatus Logico-Philosophicus 1, 10n., 26 – 8, 81f., 103 – 6, 251f., 260, 276, 280, 283, 295f., 308, 333n., 335 – 40, 359n. on analysis 206 conception of a concept 211 conception of elucidation see Tractatus, explanation of indeﬁnables conception of language 224f. conception of an object 26, 98n., 103 – 6, 118, 123f., 211, 262, 337 conception of a proposition see picture theory; also elementary proposition conception of sense 66, 161f., 254, 337f., 343 conception of simples see Tractatus, conception of an object on context principle 27, 161., 170f. and correspondence theory of truth 12, 349 – 52 explanation of indeﬁnables 27, 81f., 120 its form of representation of language 257– 63 on intentionality 122f., 255f., 335 –7 and the Investigations 303 – 6 on logically proper names 26f., 117–20, 122, 127 on the method of projection 7n., 27, 81, 149, 161, 255n. ontology of 262, 351f. on philosophy 271f., 303 – 5, 309 primacy of description in 66 psychological hinterland of 255f. on ‘this’ 110, 257f., 259f. training see language, training truth 196, 225, 278f., 336, 346 – 55 correspondence theory of 12f., 349 – 52 denominalization account of 346f. disquotational account of 346f. redundancy account of 347

394

Index

truth-conditional theories of meaning 33, 67, 134n., 138f., 151, 187, 230 truth-conditions 67, 138f., 139n., 176, 177 ‘Übersicht’ 307f. unconscious, the 279 understanding 9f., 14, 27, 39 – 43, 48f., 53, 132f., 148, 172, 180, 182 – 5, 206, 223, 256, 357– 85 as ability 18, 183f., 277f., 380 – 5 computational conception of see computationalism criteria of 32f., 36, 37, 38, 39f., 40 –3, 73f., 148, 152, 180 dawning of 370, 382 degrees of 383 as disposition 373 – 5 dispositional/occurrent 381f. as experience 362, 363, 368f. lack of 384 as mental state 363, 371–3 new sentences 162f., 181–7, 358f. objects of 382 as process 362f., 369 –71 proper names 235 –7, 242f. sentences 69, 73f. signal of 368 as state of an apparatus 365f., 373f. sudden 357f., 361

usage 153f., 291 use see meaning and use vagueness 123, 216, 261f. verbs, dynamic/static 364 veriﬁcation 57, 135 veriﬁcationist theories of meaning Vico, G. 133n. visual image 278 von Ficker, L. 335 von Wright, G. H. 210n.

134n.

Waismann, F. 7, 56, 57, 81, 83n., 84n., 226n., 227, 297, 315, 317f., 323, 328, 347, 353n., 355n., 374, 381, 384 war 213, 221 Watts, I. 202 Weltanschauung 307, 320, 326 Weyl, H. 46 Whately, R. 203 Whewell, W. 208n. White, A. R. 375n. Whitehead, A. N. 134, 282 Wisdom, A. J. T. D. 287 ‘word for’ 142f. words, essence of 1f., 3, 4 – 6, 6 –7, 13, 15 word-clusters 177 world 262f.